Find the z interval for 4.5 < x .

Question

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Answer 1

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6.2, Problem 11P

(a)

To determine

Find the z interval for $4.5<x$ .

(a)

Expert Solution

Answer to Problem 11P

The z interval for $4.5<x$ is $z>−1.00$ .

Explanation of Solution

Calculation:

Z score:

The number of standard deviations the original measurement x is from the value of mean $μ$ is measured using the z-score or z value. The formula for z score is,

$z=x−μσ$

In the formula, x is the raw score, $μ$ is the mean and $σ$ is the standard deviation.

The variable x is red blood cell (RBC) count in millions per cubic millimetre for women. The healthy females are normally distributed with mean $μ=4.8$ and standard deviation $σ=0.3$ . Then the z score is,

$z=x−4.80.3$

For the z interval consider,

$4.5<xx>4.5$

Subtract 4.8 on both sides of the inequality.

$x−4.8>4.5−4.8x−4.8>−0.3$

Divide 0.3 on both sides of the inequality.

$x−4.80.3>−0.30.3z>−1.00$

Hence, the z interval for $4.5<x$ is $z>−1.00$ .

(b)

To determine

Find the z interval for $x<4.2$ .

(b)

Expert Solution

Answer to Problem 11P

The z interval for $x<4.2$ is $z<−2.00$ .

Explanation of Solution

Calculation:

For the z interval consider,

$x<4.2$

Subtract 4.8 on both sides of the inequality.

$x−4.8<4.2−4.8x−4.8<−0.6$

Divide 0.3 on both sides of the inequality.

$x−4.80.3<−0.60.3z<−2.00$

Hence, the z interval for $x<4.2$ is $z<−2.00$ .

(c)

To determine

Find the z interval for $4.0<x<5.5$ .

(c)

Expert Solution

Answer to Problem 11P

The z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

Explanation of Solution

Calculation:

For the z interval consider,

$4.0<x<5.5$

Subtract 4.8 for each part of the inequality.

$4.0−4.8<x−4.8<5.5−4.8−0.8<x−4.8<0.7$

Divide 4.3 for each part of the inequality.

$−0.80.3<x−4.80.3<0.70.3−2.67<z<2.33$

Hence, the z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

(d)

To determine

Find the x interval for $z<−1.44$ .

(d)

Expert Solution

Answer to Problem 11P

The x interval for $z<−1.44$ is $x<4.4$ .

Explanation of Solution

Calculation:

The z score is,

$z=x−4.80.3x=4.8+0.3z$

For the x interval consider,

$z<−1.44$

Multiply 0.3 on both sides of the inequality.

$0.3z<−1.44(0.3)0.3z<−0.432$

Add 4.8 on both sides of the inequality.

$4.8+0.3z<−0.432+4.8x<4.4$

Hence, the x interval for $z<−1.44$ is $x<4.4$ .

(e)

To determine

Find the x interval for $1.28<z$ .

(e)

Expert Solution

Answer to Problem 11P

The x interval for $1.28<z$ is $x>5.2$ .

Explanation of Solution

Calculation:

For the x interval consider,

$1.28<zz>1.28$

Multiply 0.3 on both sides of the inequality.

$0.3z>1.28(0.3)0.3z>0.384$

Add 4.8 on both sides of the inequality.

$4.8+0.3z>0.384+4.8x>5.2$

Hence, the x interval for $1.28<z$ is $x>5.2$ .

(f)

To determine

Find the x interval for $−2.25<z<−1.00$ .

(f)

Expert Solution

Answer to Problem 11P

The x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

Explanation of Solution

Calculation:

For the x interval consider,

$−2.25<z<−1.00$

Multiply 0.3 for each part of the inequality.

$−2.25(0.3)<0.3z<−1.00(0.3)−0.675<0.3z<−0.300$

Add 4.8 for each part of the inequality.

$−0.675+4.8<4.8+0.3z<−0.300+4.84.12<x<4.50$

Hence, the x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

(g)

To determine

Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.

(g)

Expert Solution

Answer to Problem 11P

The RBC count of 5.9 or higher is unusually high.

Explanation of Solution

Calculation:

The RBC count of 5.9 or higher, that is $x≥5.9$ . Then the value of z is,

$x≥5.9$

Subtract 4.8 on both sides of the inequality.

$x−4.8≥5.9−4.8x−4.8≥1.1$

Divide 0.3 on both sides of the inequality.

$x−4.80.3≥1.10.3z≥3.67$

The RBC count of 5.9 or higher is 3.67 standard deviations above the mean value. The z score value is greater than 3 indicating that the value is very unusual.

The figure 6-15 is the standard normal distribution curve. The z value is located on the curve as below.

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 6.2, Problem 11P

The z value that is far from the mean (zero) is considered as unusual. If the value is closer to –3 is usually very small and value closer to 3 is usually very large.

If the value of z for RBC count of 5.9 or higher is greater to 3 then RBC count would be very large and unusual.

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Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6.2, Problem 11P

(a)

To determine

Find the z interval for $4.5<x$ .

(a)

Expert Solution

Answer to Problem 11P

The z interval for $4.5<x$ is $z>−1.00$ .

Explanation of Solution

Calculation:

Z score:

The number of standard deviations the original measurement x is from the value of mean $μ$ is measured using the z-score or z value. The formula for z score is,

$z=x−μσ$

In the formula, x is the raw score, $μ$ is the mean and $σ$ is the standard deviation.

The variable x is red blood cell (RBC) count in millions per cubic millimetre for women. The healthy females are normally distributed with mean $μ=4.8$ and standard deviation $σ=0.3$ . Then the z score is,

$z=x−4.80.3$

For the z interval consider,

$4.5<xx>4.5$

Subtract 4.8 on both sides of the inequality.

$x−4.8>4.5−4.8x−4.8>−0.3$

Divide 0.3 on both sides of the inequality.

$x−4.80.3>−0.30.3z>−1.00$

Hence, the z interval for $4.5<x$ is $z>−1.00$ .

(b)

To determine

Find the z interval for $x<4.2$ .

(b)

Expert Solution

Answer to Problem 11P

The z interval for $x<4.2$ is $z<−2.00$ .

Explanation of Solution

Calculation:

For the z interval consider,

$x<4.2$

Subtract 4.8 on both sides of the inequality.

$x−4.8<4.2−4.8x−4.8<−0.6$

Divide 0.3 on both sides of the inequality.

$x−4.80.3<−0.60.3z<−2.00$

Hence, the z interval for $x<4.2$ is $z<−2.00$ .

(c)

To determine

Find the z interval for $4.0<x<5.5$ .

(c)

Expert Solution

Answer to Problem 11P

The z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

Explanation of Solution

Calculation:

For the z interval consider,

$4.0<x<5.5$

Subtract 4.8 for each part of the inequality.

$4.0−4.8<x−4.8<5.5−4.8−0.8<x−4.8<0.7$

Divide 4.3 for each part of the inequality.

$−0.80.3<x−4.80.3<0.70.3−2.67<z<2.33$

Hence, the z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

(d)

To determine

Find the x interval for $z<−1.44$ .

(d)

Expert Solution

Answer to Problem 11P

The x interval for $z<−1.44$ is $x<4.4$ .

Explanation of Solution

Calculation:

The z score is,

$z=x−4.80.3x=4.8+0.3z$

For the x interval consider,

$z<−1.44$

Multiply 0.3 on both sides of the inequality.

$0.3z<−1.44(0.3)0.3z<−0.432$

Add 4.8 on both sides of the inequality.

$4.8+0.3z<−0.432+4.8x<4.4$

Hence, the x interval for $z<−1.44$ is $x<4.4$ .

(e)

To determine

Find the x interval for $1.28<z$ .

(e)

Expert Solution

Answer to Problem 11P

The x interval for $1.28<z$ is $x>5.2$ .

Explanation of Solution

Calculation:

For the x interval consider,

$1.28<zz>1.28$

Multiply 0.3 on both sides of the inequality.

$0.3z>1.28(0.3)0.3z>0.384$

Add 4.8 on both sides of the inequality.

$4.8+0.3z>0.384+4.8x>5.2$

Hence, the x interval for $1.28<z$ is $x>5.2$ .

(f)

To determine

Find the x interval for $−2.25<z<−1.00$ .

(f)

Expert Solution

Answer to Problem 11P

The x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

Explanation of Solution

Calculation:

For the x interval consider,

$−2.25<z<−1.00$

Multiply 0.3 for each part of the inequality.

$−2.25(0.3)<0.3z<−1.00(0.3)−0.675<0.3z<−0.300$

Add 4.8 for each part of the inequality.

$−0.675+4.8<4.8+0.3z<−0.300+4.84.12<x<4.50$

Hence, the x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

(g)

To determine

Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.

(g)

Expert Solution

Answer to Problem 11P

The RBC count of 5.9 or higher is unusually high.

Explanation of Solution

Calculation:

The RBC count of 5.9 or higher, that is $x≥5.9$ . Then the value of z is,

$x≥5.9$

Subtract 4.8 on both sides of the inequality.

$x−4.8≥5.9−4.8x−4.8≥1.1$

Divide 0.3 on both sides of the inequality.

$x−4.80.3≥1.10.3z≥3.67$

The RBC count of 5.9 or higher is 3.67 standard deviations above the mean value. The z score value is greater than 3 indicating that the value is very unusual.

The figure 6-15 is the standard normal distribution curve. The z value is located on the curve as below.

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 6.2, Problem 11P

The z value that is far from the mean (zero) is considered as unusual. If the value is closer to –3 is usually very small and value closer to 3 is usually very large.

If the value of z for RBC count of 5.9 or higher is greater to 3 then RBC count would be very large and unusual.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6.2, Problem 11P

(a)

To determine

Find the z interval for $4.5<x$ .

(a)

Expert Solution

Answer to Problem 11P

The z interval for $4.5<x$ is $z>−1.00$ .

Explanation of Solution

Calculation:

Z score:

The number of standard deviations the original measurement x is from the value of mean $μ$ is measured using the z-score or z value. The formula for z score is,

$z=x−μσ$

In the formula, x is the raw score, $μ$ is the mean and $σ$ is the standard deviation.

The variable x is red blood cell (RBC) count in millions per cubic millimetre for women. The healthy females are normally distributed with mean $μ=4.8$ and standard deviation $σ=0.3$ . Then the z score is,

$z=x−4.80.3$

For the z interval consider,

$4.5<xx>4.5$

Subtract 4.8 on both sides of the inequality.

$x−4.8>4.5−4.8x−4.8>−0.3$

Divide 0.3 on both sides of the inequality.

$x−4.80.3>−0.30.3z>−1.00$

Hence, the z interval for $4.5<x$ is $z>−1.00$ .

(b)

To determine

Find the z interval for $x<4.2$ .

(b)

Expert Solution

Answer to Problem 11P

The z interval for $x<4.2$ is $z<−2.00$ .

Explanation of Solution

Calculation:

For the z interval consider,

$x<4.2$

Subtract 4.8 on both sides of the inequality.

$x−4.8<4.2−4.8x−4.8<−0.6$

Divide 0.3 on both sides of the inequality.

$x−4.80.3<−0.60.3z<−2.00$

Hence, the z interval for $x<4.2$ is $z<−2.00$ .

(c)

To determine

Find the z interval for $4.0<x<5.5$ .

(c)

Expert Solution

Answer to Problem 11P

The z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

Explanation of Solution

Calculation:

For the z interval consider,

$4.0<x<5.5$

Subtract 4.8 for each part of the inequality.

$4.0−4.8<x−4.8<5.5−4.8−0.8<x−4.8<0.7$

Divide 4.3 for each part of the inequality.

$−0.80.3<x−4.80.3<0.70.3−2.67<z<2.33$

Hence, the z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

(d)

To determine

Find the x interval for $z<−1.44$ .

(d)

Expert Solution

Answer to Problem 11P

The x interval for $z<−1.44$ is $x<4.4$ .

Explanation of Solution

Calculation:

The z score is,

$z=x−4.80.3x=4.8+0.3z$

For the x interval consider,

$z<−1.44$

Multiply 0.3 on both sides of the inequality.

$0.3z<−1.44(0.3)0.3z<−0.432$

Add 4.8 on both sides of the inequality.

$4.8+0.3z<−0.432+4.8x<4.4$

Hence, the x interval for $z<−1.44$ is $x<4.4$ .

(e)

To determine

Find the x interval for $1.28<z$ .

(e)

Expert Solution

Answer to Problem 11P

The x interval for $1.28<z$ is $x>5.2$ .

Explanation of Solution

Calculation:

For the x interval consider,

$1.28<zz>1.28$

Multiply 0.3 on both sides of the inequality.

$0.3z>1.28(0.3)0.3z>0.384$

Add 4.8 on both sides of the inequality.

$4.8+0.3z>0.384+4.8x>5.2$

Hence, the x interval for $1.28<z$ is $x>5.2$ .

(f)

To determine

Find the x interval for $−2.25<z<−1.00$ .

(f)

Expert Solution

Answer to Problem 11P

The x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

Explanation of Solution

Calculation:

For the x interval consider,

$−2.25<z<−1.00$

Multiply 0.3 for each part of the inequality.

$−2.25(0.3)<0.3z<−1.00(0.3)−0.675<0.3z<−0.300$

Add 4.8 for each part of the inequality.

$−0.675+4.8<4.8+0.3z<−0.300+4.84.12<x<4.50$

Hence, the x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

(g)

To determine

Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.

(g)

Expert Solution

Answer to Problem 11P

The RBC count of 5.9 or higher is unusually high.

Explanation of Solution

Calculation:

The RBC count of 5.9 or higher, that is $x≥5.9$ . Then the value of z is,

$x≥5.9$

Subtract 4.8 on both sides of the inequality.

$x−4.8≥5.9−4.8x−4.8≥1.1$

Divide 0.3 on both sides of the inequality.

$x−4.80.3≥1.10.3z≥3.67$

The RBC count of 5.9 or higher is 3.67 standard deviations above the mean value. The z score value is greater than 3 indicating that the value is very unusual.

The figure 6-15 is the standard normal distribution curve. The z value is located on the curve as below.

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 6.2, Problem 11P

The z value that is far from the mean (zero) is considered as unusual. If the value is closer to –3 is usually very small and value closer to 3 is usually very large.

If the value of z for RBC count of 5.9 or higher is greater to 3 then RBC count would be very large and unusual.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6.2, Problem 11P

(a)

To determine

Find the z interval for $4.5<x$ .

(a)

Expert Solution

Answer to Problem 11P

The z interval for $4.5<x$ is $z>−1.00$ .

Explanation of Solution

Calculation:

Z score:

The number of standard deviations the original measurement x is from the value of mean $μ$ is measured using the z-score or z value. The formula for z score is,

$z=x−μσ$

In the formula, x is the raw score, $μ$ is the mean and $σ$ is the standard deviation.

The variable x is red blood cell (RBC) count in millions per cubic millimetre for women. The healthy females are normally distributed with mean $μ=4.8$ and standard deviation $σ=0.3$ . Then the z score is,

$z=x−4.80.3$

For the z interval consider,

$4.5<xx>4.5$

Subtract 4.8 on both sides of the inequality.

$x−4.8>4.5−4.8x−4.8>−0.3$

Divide 0.3 on both sides of the inequality.

$x−4.80.3>−0.30.3z>−1.00$

Hence, the z interval for $4.5<x$ is $z>−1.00$ .

(b)

To determine

Find the z interval for $x<4.2$ .

(b)

Expert Solution

Answer to Problem 11P

The z interval for $x<4.2$ is $z<−2.00$ .

Explanation of Solution

Calculation:

For the z interval consider,

$x<4.2$

Subtract 4.8 on both sides of the inequality.

$x−4.8<4.2−4.8x−4.8<−0.6$

Divide 0.3 on both sides of the inequality.

$x−4.80.3<−0.60.3z<−2.00$

Hence, the z interval for $x<4.2$ is $z<−2.00$ .

(c)

To determine

Find the z interval for $4.0<x<5.5$ .

(c)

Expert Solution

Answer to Problem 11P

The z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

Explanation of Solution

Calculation:

For the z interval consider,

$4.0<x<5.5$

Subtract 4.8 for each part of the inequality.

$4.0−4.8<x−4.8<5.5−4.8−0.8<x−4.8<0.7$

Divide 4.3 for each part of the inequality.

$−0.80.3<x−4.80.3<0.70.3−2.67<z<2.33$

Hence, the z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

(d)

To determine

Find the x interval for $z<−1.44$ .

(d)

Expert Solution

Answer to Problem 11P

The x interval for $z<−1.44$ is $x<4.4$ .

Explanation of Solution

Calculation:

The z score is,

$z=x−4.80.3x=4.8+0.3z$

For the x interval consider,

$z<−1.44$

Multiply 0.3 on both sides of the inequality.

$0.3z<−1.44(0.3)0.3z<−0.432$

Add 4.8 on both sides of the inequality.

$4.8+0.3z<−0.432+4.8x<4.4$

Hence, the x interval for $z<−1.44$ is $x<4.4$ .

(e)

To determine

Find the x interval for $1.28<z$ .

(e)

Expert Solution

Answer to Problem 11P

The x interval for $1.28<z$ is $x>5.2$ .

Explanation of Solution

Calculation:

For the x interval consider,

$1.28<zz>1.28$

Multiply 0.3 on both sides of the inequality.

$0.3z>1.28(0.3)0.3z>0.384$

Add 4.8 on both sides of the inequality.

$4.8+0.3z>0.384+4.8x>5.2$

Hence, the x interval for $1.28<z$ is $x>5.2$ .

(f)

To determine

Find the x interval for $−2.25<z<−1.00$ .

(f)

Expert Solution

Answer to Problem 11P

The x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

Explanation of Solution

Calculation:

For the x interval consider,

$−2.25<z<−1.00$

Multiply 0.3 for each part of the inequality.

$−2.25(0.3)<0.3z<−1.00(0.3)−0.675<0.3z<−0.300$

Add 4.8 for each part of the inequality.

$−0.675+4.8<4.8+0.3z<−0.300+4.84.12<x<4.50$

Hence, the x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

(g)

To determine

Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.

(g)

Expert Solution

Answer to Problem 11P

The RBC count of 5.9 or higher is unusually high.

Explanation of Solution

Calculation:

The RBC count of 5.9 or higher, that is $x≥5.9$ . Then the value of z is,

$x≥5.9$

Subtract 4.8 on both sides of the inequality.

$x−4.8≥5.9−4.8x−4.8≥1.1$

Divide 0.3 on both sides of the inequality.

$x−4.80.3≥1.10.3z≥3.67$

The RBC count of 5.9 or higher is 3.67 standard deviations above the mean value. The z score value is greater than 3 indicating that the value is very unusual.

The figure 6-15 is the standard normal distribution curve. The z value is located on the curve as below.

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 6.2, Problem 11P

The z value that is far from the mean (zero) is considered as unusual. If the value is closer to –3 is usually very small and value closer to 3 is usually very large.

If the value of z for RBC count of 5.9 or higher is greater to 3 then RBC count would be very large and unusual.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 6.2, Problem 11P

(a)

To determine

Find the z interval for $4.5<x$ .

(a)

Expert Solution

Answer to Problem 11P

The z interval for $4.5<x$ is $z>−1.00$ .

Explanation of Solution

Calculation:

Z score:

The number of standard deviations the original measurement x is from the value of mean $μ$ is measured using the z-score or z value. The formula for z score is,

$z=x−μσ$

In the formula, x is the raw score, $μ$ is the mean and $σ$ is the standard deviation.

The variable x is red blood cell (RBC) count in millions per cubic millimetre for women. The healthy females are normally distributed with mean $μ=4.8$ and standard deviation $σ=0.3$ . Then the z score is,

$z=x−4.80.3$

For the z interval consider,

$4.5<xx>4.5$

Subtract 4.8 on both sides of the inequality.

$x−4.8>4.5−4.8x−4.8>−0.3$

Divide 0.3 on both sides of the inequality.

$x−4.80.3>−0.30.3z>−1.00$

Hence, the z interval for $4.5<x$ is $z>−1.00$ .

(b)

To determine

Find the z interval for $x<4.2$ .

(b)

Expert Solution

Answer to Problem 11P

The z interval for $x<4.2$ is $z<−2.00$ .

Explanation of Solution

Calculation:

For the z interval consider,

$x<4.2$

Subtract 4.8 on both sides of the inequality.

$x−4.8<4.2−4.8x−4.8<−0.6$

Divide 0.3 on both sides of the inequality.

$x−4.80.3<−0.60.3z<−2.00$

Hence, the z interval for $x<4.2$ is $z<−2.00$ .

(c)

To determine

Find the z interval for $4.0<x<5.5$ .

(c)

Expert Solution

Answer to Problem 11P

The z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

Explanation of Solution

Calculation:

For the z interval consider,

$4.0<x<5.5$

Subtract 4.8 for each part of the inequality.

$4.0−4.8<x−4.8<5.5−4.8−0.8<x−4.8<0.7$

Divide 4.3 for each part of the inequality.

$−0.80.3<x−4.80.3<0.70.3−2.67<z<2.33$

Hence, the z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

(d)

To determine

Find the x interval for $z<−1.44$ .

(d)

Expert Solution

Answer to Problem 11P

The x interval for $z<−1.44$ is $x<4.4$ .

Explanation of Solution

Calculation:

The z score is,

$z=x−4.80.3x=4.8+0.3z$

For the x interval consider,

$z<−1.44$

Multiply 0.3 on both sides of the inequality.

$0.3z<−1.44(0.3)0.3z<−0.432$

Add 4.8 on both sides of the inequality.

$4.8+0.3z<−0.432+4.8x<4.4$

Hence, the x interval for $z<−1.44$ is $x<4.4$ .

(e)

To determine

Find the x interval for $1.28<z$ .

(e)

Expert Solution

Answer to Problem 11P

The x interval for $1.28<z$ is $x>5.2$ .

Explanation of Solution

Calculation:

For the x interval consider,

$1.28<zz>1.28$

Multiply 0.3 on both sides of the inequality.

$0.3z>1.28(0.3)0.3z>0.384$

Add 4.8 on both sides of the inequality.

$4.8+0.3z>0.384+4.8x>5.2$

Hence, the x interval for $1.28<z$ is $x>5.2$ .

(f)

To determine

Find the x interval for $−2.25<z<−1.00$ .

(f)

Expert Solution

Answer to Problem 11P

The x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

Explanation of Solution

Calculation:

For the x interval consider,

$−2.25<z<−1.00$

Multiply 0.3 for each part of the inequality.

$−2.25(0.3)<0.3z<−1.00(0.3)−0.675<0.3z<−0.300$

Add 4.8 for each part of the inequality.

$−0.675+4.8<4.8+0.3z<−0.300+4.84.12<x<4.50$

Hence, the x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

(g)

To determine

Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.

(g)

Expert Solution

Answer to Problem 11P

The RBC count of 5.9 or higher is unusually high.

Explanation of Solution

Calculation:

The RBC count of 5.9 or higher, that is $x≥5.9$ . Then the value of z is,

$x≥5.9$

Subtract 4.8 on both sides of the inequality.

$x−4.8≥5.9−4.8x−4.8≥1.1$

Divide 0.3 on both sides of the inequality.

$x−4.80.3≥1.10.3z≥3.67$

The RBC count of 5.9 or higher is 3.67 standard deviations above the mean value. The z score value is greater than 3 indicating that the value is very unusual.

The figure 6-15 is the standard normal distribution curve. The z value is located on the curve as below.

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 6.2, Problem 11P

The z value that is far from the mean (zero) is considered as unusual. If the value is closer to –3 is usually very small and value closer to 3 is usually very large.

If the value of z for RBC count of 5.9 or higher is greater to 3 then RBC count would be very large and unusual.

Answer 6

Chapter 6.2, Problem 11P

(a)

To determine

Find the z interval for $4.5<x$ .

(a)

Expert Solution

Answer to Problem 11P

The z interval for $4.5<x$ is $z>−1.00$ .

Explanation of Solution

Calculation:

Z score:

The number of standard deviations the original measurement x is from the value of mean $μ$ is measured using the z-score or z value. The formula for z score is,

$z=x−μσ$

In the formula, x is the raw score, $μ$ is the mean and $σ$ is the standard deviation.

The variable x is red blood cell (RBC) count in millions per cubic millimetre for women. The healthy females are normally distributed with mean $μ=4.8$ and standard deviation $σ=0.3$ . Then the z score is,

$z=x−4.80.3$

For the z interval consider,

$4.5<xx>4.5$

Subtract 4.8 on both sides of the inequality.

$x−4.8>4.5−4.8x−4.8>−0.3$

Divide 0.3 on both sides of the inequality.

$x−4.80.3>−0.30.3z>−1.00$

Hence, the z interval for $4.5<x$ is $z>−1.00$ .

Answer 7

Chapter 6.2, Problem 11P

(a)

To determine

Find the z interval for $4.5<x$ .

Answer 8

(a)

Expert Solution

Answer to Problem 11P

The z interval for $4.5<x$ is $z>−1.00$ .

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation:

Z score:

The number of standard deviations the original measurement x is from the value of mean $μ$ is measured using the z-score or z value. The formula for z score is,

$z=x−μσ$

In the formula, x is the raw score, $μ$ is the mean and $σ$ is the standard deviation.

The variable x is red blood cell (RBC) count in millions per cubic millimetre for women. The healthy females are normally distributed with mean $μ=4.8$ and standard deviation $σ=0.3$ . Then the z score is,

$z=x−4.80.3$

For the z interval consider,

$4.5<xx>4.5$

Subtract 4.8 on both sides of the inequality.

$x−4.8>4.5−4.8x−4.8>−0.3$

Divide 0.3 on both sides of the inequality.

$x−4.80.3>−0.30.3z>−1.00$

Hence, the z interval for $4.5<x$ is $z>−1.00$ .

Answer 13

(b)

To determine

Find the z interval for $x<4.2$ .

(b)

Expert Solution

Answer to Problem 11P

The z interval for $x<4.2$ is $z<−2.00$ .

Explanation of Solution

Calculation:

For the z interval consider,

$x<4.2$

Subtract 4.8 on both sides of the inequality.

$x−4.8<4.2−4.8x−4.8<−0.6$

Divide 0.3 on both sides of the inequality.

$x−4.80.3<−0.60.3z<−2.00$

Hence, the z interval for $x<4.2$ is $z<−2.00$ .

Answer 14

(b)

To determine

Find the z interval for $x<4.2$ .

Answer 15

(b)

Expert Solution

Answer to Problem 11P

The z interval for $x<4.2$ is $z<−2.00$ .

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Calculation:

For the z interval consider,

$x<4.2$

Subtract 4.8 on both sides of the inequality.

$x−4.8<4.2−4.8x−4.8<−0.6$

Divide 0.3 on both sides of the inequality.

$x−4.80.3<−0.60.3z<−2.00$

Hence, the z interval for $x<4.2$ is $z<−2.00$ .

Answer 20

(c)

To determine

Find the z interval for $4.0<x<5.5$ .

(c)

Expert Solution

Answer to Problem 11P

The z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

Explanation of Solution

Calculation:

For the z interval consider,

$4.0<x<5.5$

Subtract 4.8 for each part of the inequality.

$4.0−4.8<x−4.8<5.5−4.8−0.8<x−4.8<0.7$

Divide 4.3 for each part of the inequality.

$−0.80.3<x−4.80.3<0.70.3−2.67<z<2.33$

Hence, the z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

Answer 21

(c)

To determine

Find the z interval for $4.0<x<5.5$ .

Answer 22

(c)

Expert Solution

Answer to Problem 11P

The z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Calculation:

For the z interval consider,

$4.0<x<5.5$

Subtract 4.8 for each part of the inequality.

$4.0−4.8<x−4.8<5.5−4.8−0.8<x−4.8<0.7$

Divide 4.3 for each part of the inequality.

$−0.80.3<x−4.80.3<0.70.3−2.67<z<2.33$

Hence, the z interval for $4.0<x<5.5$ is $−2.67<z<2.33$ .

Answer 27

(d)

To determine

Find the x interval for $z<−1.44$ .

(d)

Expert Solution

Answer to Problem 11P

The x interval for $z<−1.44$ is $x<4.4$ .

Explanation of Solution

Calculation:

The z score is,

$z=x−4.80.3x=4.8+0.3z$

For the x interval consider,

$z<−1.44$

Multiply 0.3 on both sides of the inequality.

$0.3z<−1.44(0.3)0.3z<−0.432$

Add 4.8 on both sides of the inequality.

$4.8+0.3z<−0.432+4.8x<4.4$

Hence, the x interval for $z<−1.44$ is $x<4.4$ .

Answer 28

(d)

To determine

Find the x interval for $z<−1.44$ .

Answer 29

(d)

Expert Solution

Answer to Problem 11P

The x interval for $z<−1.44$ is $x<4.4$ .

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Calculation:

The z score is,

$z=x−4.80.3x=4.8+0.3z$

For the x interval consider,

$z<−1.44$

Multiply 0.3 on both sides of the inequality.

$0.3z<−1.44(0.3)0.3z<−0.432$

Add 4.8 on both sides of the inequality.

$4.8+0.3z<−0.432+4.8x<4.4$

Hence, the x interval for $z<−1.44$ is $x<4.4$ .

Answer 34

(e)

To determine

Find the x interval for $1.28<z$ .

(e)

Expert Solution

Answer to Problem 11P

The x interval for $1.28<z$ is $x>5.2$ .

Explanation of Solution

Calculation:

For the x interval consider,

$1.28<zz>1.28$

Multiply 0.3 on both sides of the inequality.

$0.3z>1.28(0.3)0.3z>0.384$

Add 4.8 on both sides of the inequality.

$4.8+0.3z>0.384+4.8x>5.2$

Hence, the x interval for $1.28<z$ is $x>5.2$ .

Answer 35

(e)

To determine

Find the x interval for $1.28<z$ .

Answer 36

(e)

Expert Solution

Answer to Problem 11P

The x interval for $1.28<z$ is $x>5.2$ .

Answer 37

(e)

Expert Solution

Answer 38

(e)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Calculation:

For the x interval consider,

$1.28<zz>1.28$

Multiply 0.3 on both sides of the inequality.

$0.3z>1.28(0.3)0.3z>0.384$

Add 4.8 on both sides of the inequality.

$4.8+0.3z>0.384+4.8x>5.2$

Hence, the x interval for $1.28<z$ is $x>5.2$ .

Answer 41

(f)

To determine

Find the x interval for $−2.25<z<−1.00$ .

(f)

Expert Solution

Answer to Problem 11P

The x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

Explanation of Solution

Calculation:

For the x interval consider,

$−2.25<z<−1.00$

Multiply 0.3 for each part of the inequality.

$−2.25(0.3)<0.3z<−1.00(0.3)−0.675<0.3z<−0.300$

Add 4.8 for each part of the inequality.

$−0.675+4.8<4.8+0.3z<−0.300+4.84.12<x<4.50$

Hence, the x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

Answer 42

(f)

To determine

Find the x interval for $−2.25<z<−1.00$ .

Answer 43

(f)

Expert Solution

Answer to Problem 11P

The x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

Answer 44

(f)

Expert Solution

Answer 45

(f)

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

Calculation:

For the x interval consider,

$−2.25<z<−1.00$

Multiply 0.3 for each part of the inequality.

$−2.25(0.3)<0.3z<−1.00(0.3)−0.675<0.3z<−0.300$

Add 4.8 for each part of the inequality.

$−0.675+4.8<4.8+0.3z<−0.300+4.84.12<x<4.50$

Hence, the x interval for $−2.25<z<−1.00$ is $4.12<x<4.50$ .

Answer 48

(g)

To determine

Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.

(g)

Expert Solution

Answer to Problem 11P

The RBC count of 5.9 or higher is unusually high.

Explanation of Solution

Calculation:

The RBC count of 5.9 or higher, that is $x≥5.9$ . Then the value of z is,

$x≥5.9$

Subtract 4.8 on both sides of the inequality.

$x−4.8≥5.9−4.8x−4.8≥1.1$

Divide 0.3 on both sides of the inequality.

$x−4.80.3≥1.10.3z≥3.67$

The RBC count of 5.9 or higher is 3.67 standard deviations above the mean value. The z score value is greater than 3 indicating that the value is very unusual.

The figure 6-15 is the standard normal distribution curve. The z value is located on the curve as below.

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 6.2, Problem 11P

The z value that is far from the mean (zero) is considered as unusual. If the value is closer to –3 is usually very small and value closer to 3 is usually very large.

If the value of z for RBC count of 5.9 or higher is greater to 3 then RBC count would be very large and unusual.

Answer 49

(g)

To determine

Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.

Answer 50

(g)

Expert Solution

Answer to Problem 11P

The RBC count of 5.9 or higher is unusually high.

Answer 51

(g)

Expert Solution

Answer 52

(g)

Expert Solution

Answer 53

Expert Solution

Answer 54

Explanation of Solution

Calculation:

The RBC count of 5.9 or higher, that is $x≥5.9$ . Then the value of z is,

$x≥5.9$

Subtract 4.8 on both sides of the inequality.

$x−4.8≥5.9−4.8x−4.8≥1.1$

Divide 0.3 on both sides of the inequality.

$x−4.80.3≥1.10.3z≥3.67$

The RBC count of 5.9 or higher is 3.67 standard deviations above the mean value. The z score value is greater than 3 indicating that the value is very unusual.

The figure 6-15 is the standard normal distribution curve. The z value is located on the curve as below.

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 6.2, Problem 11P

The z value that is far from the mean (zero) is considered as unusual. If the value is closer to –3 is usually very small and value closer to 3 is usually very large.

If the value of z for RBC count of 5.9 or higher is greater to 3 then RBC count would be very large and unusual.

Answer 55

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Find the z interval for 4.5 < x .

Concept explainers

Videos

Find the z interval for $4.5<x$ .

Answer to Problem 11P

Explanation of Solution

Find the z interval for $x<4.2$ .

Answer to Problem 11P

Explanation of Solution

Find the z interval for $4.0<x<5.5$ .

Answer to Problem 11P

Explanation of Solution

Find the x interval for $z<−1.44$ .

Answer to Problem 11P

Explanation of Solution

Find the x interval for $1.28<z$ .

Answer to Problem 11P

Explanation of Solution

Find the x interval for $−2.25<z<−1.00$ .

Answer to Problem 11P

Explanation of Solution

Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.

Answer to Problem 11P

Explanation of Solution

Want to see more full solutions like this?

Chapter 6 Solutions

Find the z interval for 4.5 &lt; x .

Concept explainers

Videos

Find the z interval for 4.5<x<m:math><m:mrow><m:mn>4.5</m:mn><m:mo>&lt;</m:mo><m:mi>x</m:mi></m:mrow></m:math>.

Answer to Problem 11P

Explanation of Solution

Find the z interval for x<4.2<m:math><m:mrow><m:mi>x</m:mi><m:mo>&lt;</m:mo><m:mn>4.2</m:mn></m:mrow></m:math>.

Answer to Problem 11P

Explanation of Solution

Find the z interval for 4.0<x<5.5<m:math><m:mrow><m:mn>4.0</m:mn><m:mo>&lt;</m:mo><m:mi>x</m:mi><m:mo>&lt;</m:mo><m:mn>5.5</m:mn></m:mrow></m:math>.

Answer to Problem 11P

Explanation of Solution

Find the x interval for z<−1.44<m:math><m:mrow><m:mi>z</m:mi><m:mo>&lt;</m:mo><m:mo>−</m:mo><m:mn>1.44</m:mn></m:mrow></m:math>.

Answer to Problem 11P

Explanation of Solution

Find the x interval for 1.28<z<m:math><m:mrow><m:mn>1.28</m:mn><m:mo>&lt;</m:mo><m:mi>z</m:mi></m:mrow></m:math>.

Answer to Problem 11P

Explanation of Solution

Find the x interval for −2.25<z<−1.00<m:math><m:mrow><m:mo>−</m:mo><m:mn>2.25</m:mn><m:mo>&lt;</m:mo><m:mi>z</m:mi><m:mo>&lt;</m:mo><m:mo>−</m:mo><m:mn>1.00</m:mn></m:mrow></m:math>.

Answer to Problem 11P

Explanation of Solution

Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.

Answer to Problem 11P

Explanation of Solution

Want to see more full solutions like this?

Chapter 6 Solutions

Find the z interval for 4.5 < x .

Find the z interval for $4.5<x$ .

Find the z interval for $x<4.2$ .

Find the z interval for $4.0<x<5.5$ .

Find the x interval for $z<−1.44$ .

Find the x interval for $1.28<z$ .

Find the x interval for $−2.25<z<−1.00$ .