Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
3rd Edition
ISBN: 9781259969454
Author: William Navidi Prof.; Barry Monk Professor
Publisher: McGraw-Hill Education
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Chapter 7.2, Problem 28E

Baby weights: According to a recent National Health Statistics Reports: the weight of male babies less than 2 months old in the United States is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds.

  1. What proportion of babies weigh more than 13 pounds?
  2. What proportion of babies weigh less than 15 pounds?
  3. What proportion of babies weigh between 10 and 14 pounds?
  4. Is it unusual for a baby to weigh more than 17 pounds?

a.

Expert Solution
Check Mark
To determine

To find: The proportion of baby weighs more than 13 pounds.

Answer to Problem 28E

The proportion of baby weigh more than 13 poundsis 28.77% .

Explanation of Solution

Given information:The mean is 11.5 and standard of deviation is 2.7 .

Formula used:

  Z=x-μσ

Here, the mean is μ and standard of deviation is σ .

Calculation:

Consider the formula for Z value.

  Z=x-μσ …….. (1)

Substitute 13 for x , 11.5 for μ and 2.7 for σ in Equation (1).

  Z=1311.52.7=0.56

From the table of standard normal distribution, for the Z value less than 0.56 the value of proportion is 0.71226 .

The proportion of baby weighs more than 13 poundsis,

  P(X>13)=1P(Z<13) …….. (2)

Substitute the values in above equation.

  P(X>13)=10.71226=0.28774=28.77%

Therefore, the proportion of baby weigh more than 13 poundsis 28.77% .

b.

Expert Solution
Check Mark
To determine

To find:The proportion of baby weighs less than 15 pounds.

Answer to Problem 28E

The proportion of baby weighs less than 15 poundsis 90.32% .

Explanation of Solution

Given information:The mean is 11.5 and standard of deviation is 2.7 .

Formula used:

  Z=x-μσ

Here, the mean is μ and standard of deviation is σ .

Calculation:

Consider the formula for Z value.

  Z=x-μσ …….. (1)

Substitute 15 for x , 11.5 for μ and 2.7 for σ in Equation (1).

  Z=1511.52.7=1.30

From the table of standard normal distribution, for the Z value less than 1.30 the value of proportion is 0.90320 .

Therefore, the proportion of baby weighs less than 15 pounds is 90.32% .

c.

Expert Solution
Check Mark
To determine

To find: The proportion of baby weighs between 10 and 14 pounds.

Answer to Problem 28E

The proportion of baby weighs between 10 and 14 poundsis 53.61% .

Explanation of Solution

Given information:The mean is 11.5 and standard of deviation is 2.7 .

Formula used:

  Z=x-μσ

Here, the mean is μ and standard of deviation is σ .

Calculation:

Consider the formula for Z value.

  Z=x-μσ …….. (1)

Substitute 14 for x , 11.5 for μ and 2.7 for σ in Equation (1).

  Z=1411.52.7=0.93

From the table of standard normal distribution, for the Z value less than 0.93 the value of proportion is 0.82381 .

Substitute 10 for x , 11.5 for μ and 2.7 for σ in Equation (1).

  Z=1011.52.7=0.56

From the table of standard normal distribution, for the Z value greater than 0.56 the value of proportion is 0.28774 .

The proportion of baby weighs between 10 and 14 poundsis,

  P(10<X<14)=P(Z<14)P(Z>10) …….. (2)

Substitute the values in above equation.

  P(10<X<14)=0.823810.28774=0.53607=53.61%

Therefore, the proportion of baby weighs between 10 and 14 poundsis 16.85% .

d.

Expert Solution
Check Mark
To determine

To find:Whether it is unusual for a baby to weigh morethan 17 .

Answer to Problem 28E

It is unusual for a baby to weigh more than 17 .

Explanation of Solution

Given information:The mean is 11.5 and standard of deviation is 2.7 .

Calculation:

The point value of mean is,

  μ±2σ=11.5±2(2.7)=6.1,16.9 …….. (1)

Since, the value do not lies in between the interval.

Therefore, it is unusual for a baby to weigh more than 17 .

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Chapter 7 Solutions

Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561

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