Themean for the average number of friends per user for the provided sample.

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 5.1, Problem 20E

(a)

Section 1:

To determine

To find: Themean for the average number of friends per user for the provided sample.

(a)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is 190friends.

Explanation of Solution

The sample mean of average number of friends per user is calculated by the formula as:

$μx¯=∑i=1n=70x¯in=x¯1+x¯2+..+x¯69+x¯7070=190+190+...+19070=190$

It is provided that average number of friends on Facebook for eachuser is 190and the sample of70adult users is taken. Hence, the mean of the average number of friends per adult user is 190friends.

Section 2:

To determine

To find: The sample standard deviationfor the mean number of friends per adult user.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The sample standard deviation is $34.423$ .

Explanation of Solution

The standard deviation of sample means is calculated by the formula as:

$σx¯=σn=28870=34.423$

Hence, the sample standard deviation of mean of numbers friends per adult user is $34.423$ .

(b)

To determine

To find: The probability that the average number of friends for 70 Facebook users is greater than 250.

(b)

Expert Solution

Answer to Problem 20E

Solution: The probability is $0.0409$ .

Explanation of Solution

The probability that the average number of friends for 70Facebook users is greater than 250will be given by:

$P(x¯>250)$

The probability that $x¯$ is greater than 250is the area to the right of the normal curve. To find the area, first convert the value of sample mean $x¯>250$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 250is calculated as:

$P(x¯>250)=P(x¯−μσ/n>250−190288/70)=P(z>1.74)=1−P(z≤1.74)=1−0.9591=0.0409$

The area under the curveto the right of $P(z≤1.74)$ by using the standard normal table is obtained as $0.0409$ .

Therefore, the required probability that the sample of 70 Facebook users has minimum of 250 friends is $0.0409$ .

(c)

Section 1:

To determine

To find: The mean of total number of friends in the provided sample.

(c)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is27040.

Explanation of Solution

The sample mean of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample mean of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as::

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the mean of total number of friends in the sample is 13300.

Section 2:

To determine

To find: The standard deviation of total number of friends in the provided sample.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The standard deviation is 288.

Explanation of Solution

The sample standard deviation of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample standard deviation of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as:

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the standard deviation of total number of friends is calculated as:

$82946.01=288$

(d)

To determine

To find: The probability that the total number of friends for 70Facebook users is greater than 17500.

(d)

Expert Solution

Answer to Problem 20E

Solution: The probability is $1$ .

Explanation of Solution

The required probability that the mean of total number of friends of 70users is greater than 17500; that is the required probability will be given by:

$∑i=170xi≈N(70×190,70×34.4232)y=∑i=170xi≈N(13300,82946.01)$

The probability that $y$ is greater than 17500is the area to the right of the normal curve. To find the area, first convert the value of sample mean $y>17500$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 17500is calculated as:

$P(Y>17500)=P(y−μσ>17500−13300288)=P(z>−14.58)=1−P(z≤−14.58)=1$

The area under the curve to the right of $P(z≤−14.58)$ is obtained as 0.000 from the standard normal table.

Therefore, the obtained probability is 1.

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Students have asked these similar questions

1 for all k, and set o (ii) Let X1, X2, that P(Xkb) = x > 0. Xn be independent random variables with mean 0, suppose = and Var Xk. Then, for 0x) ≤2 exp-tx+121 Στ k=1

Lemma 1.1 Suppose that g is a non-negative, non-decreasing function such that E g(X) 0. Then, E g(|X|) P(|X|> x) ≤ g(x)

Proof of this Theorem Theorem 1.2 (i) Suppose that P(|X| ≤ b) = 1 for some b > 0, that E X = 0, and set Var X = o². Then, for 0 0, P(X > x) ≤ e−1x+1²², P(|X|> x) ≤ 2e−x+1² 0²

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 5.1, Problem 20E

(a)

Section 1:

To determine

To find: Themean for the average number of friends per user for the provided sample.

(a)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is 190friends.

Explanation of Solution

The sample mean of average number of friends per user is calculated by the formula as:

$μx¯=∑i=1n=70x¯in=x¯1+x¯2+..+x¯69+x¯7070=190+190+...+19070=190$

It is provided that average number of friends on Facebook for eachuser is 190and the sample of70adult users is taken. Hence, the mean of the average number of friends per adult user is 190friends.

Section 2:

To determine

To find: The sample standard deviationfor the mean number of friends per adult user.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The sample standard deviation is $34.423$ .

Explanation of Solution

The standard deviation of sample means is calculated by the formula as:

$σx¯=σn=28870=34.423$

Hence, the sample standard deviation of mean of numbers friends per adult user is $34.423$ .

(b)

To determine

To find: The probability that the average number of friends for 70 Facebook users is greater than 250.

(b)

Expert Solution

Answer to Problem 20E

Solution: The probability is $0.0409$ .

Explanation of Solution

The probability that the average number of friends for 70Facebook users is greater than 250will be given by:

$P(x¯>250)$

The probability that $x¯$ is greater than 250is the area to the right of the normal curve. To find the area, first convert the value of sample mean $x¯>250$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 250is calculated as:

$P(x¯>250)=P(x¯−μσ/n>250−190288/70)=P(z>1.74)=1−P(z≤1.74)=1−0.9591=0.0409$

The area under the curveto the right of $P(z≤1.74)$ by using the standard normal table is obtained as $0.0409$ .

Therefore, the required probability that the sample of 70 Facebook users has minimum of 250 friends is $0.0409$ .

(c)

Section 1:

To determine

To find: The mean of total number of friends in the provided sample.

(c)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is27040.

Explanation of Solution

The sample mean of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample mean of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as::

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the mean of total number of friends in the sample is 13300.

Section 2:

To determine

To find: The standard deviation of total number of friends in the provided sample.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The standard deviation is 288.

Explanation of Solution

The sample standard deviation of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample standard deviation of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as:

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the standard deviation of total number of friends is calculated as:

$82946.01=288$

(d)

To determine

To find: The probability that the total number of friends for 70Facebook users is greater than 17500.

(d)

Expert Solution

Answer to Problem 20E

Solution: The probability is $1$ .

Explanation of Solution

The required probability that the mean of total number of friends of 70users is greater than 17500; that is the required probability will be given by:

$∑i=170xi≈N(70×190,70×34.4232)y=∑i=170xi≈N(13300,82946.01)$

The probability that $y$ is greater than 17500is the area to the right of the normal curve. To find the area, first convert the value of sample mean $y>17500$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 17500is calculated as:

$P(Y>17500)=P(y−μσ>17500−13300288)=P(z>−14.58)=1−P(z≤−14.58)=1$

The area under the curve to the right of $P(z≤−14.58)$ is obtained as 0.000 from the standard normal table.

Therefore, the obtained probability is 1.

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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 5.1, Problem 20E

(a)

Section 1:

To determine

To find: Themean for the average number of friends per user for the provided sample.

(a)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is 190friends.

Explanation of Solution

The sample mean of average number of friends per user is calculated by the formula as:

$μx¯=∑i=1n=70x¯in=x¯1+x¯2+..+x¯69+x¯7070=190+190+...+19070=190$

It is provided that average number of friends on Facebook for eachuser is 190and the sample of70adult users is taken. Hence, the mean of the average number of friends per adult user is 190friends.

Section 2:

To determine

To find: The sample standard deviationfor the mean number of friends per adult user.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The sample standard deviation is $34.423$ .

Explanation of Solution

The standard deviation of sample means is calculated by the formula as:

$σx¯=σn=28870=34.423$

Hence, the sample standard deviation of mean of numbers friends per adult user is $34.423$ .

(b)

To determine

To find: The probability that the average number of friends for 70 Facebook users is greater than 250.

(b)

Expert Solution

Answer to Problem 20E

Solution: The probability is $0.0409$ .

Explanation of Solution

The probability that the average number of friends for 70Facebook users is greater than 250will be given by:

$P(x¯>250)$

The probability that $x¯$ is greater than 250is the area to the right of the normal curve. To find the area, first convert the value of sample mean $x¯>250$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 250is calculated as:

$P(x¯>250)=P(x¯−μσ/n>250−190288/70)=P(z>1.74)=1−P(z≤1.74)=1−0.9591=0.0409$

The area under the curveto the right of $P(z≤1.74)$ by using the standard normal table is obtained as $0.0409$ .

Therefore, the required probability that the sample of 70 Facebook users has minimum of 250 friends is $0.0409$ .

(c)

Section 1:

To determine

To find: The mean of total number of friends in the provided sample.

(c)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is27040.

Explanation of Solution

The sample mean of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample mean of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as::

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the mean of total number of friends in the sample is 13300.

Section 2:

To determine

To find: The standard deviation of total number of friends in the provided sample.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The standard deviation is 288.

Explanation of Solution

The sample standard deviation of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample standard deviation of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as:

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the standard deviation of total number of friends is calculated as:

$82946.01=288$

(d)

To determine

To find: The probability that the total number of friends for 70Facebook users is greater than 17500.

(d)

Expert Solution

Answer to Problem 20E

Solution: The probability is $1$ .

Explanation of Solution

The required probability that the mean of total number of friends of 70users is greater than 17500; that is the required probability will be given by:

$∑i=170xi≈N(70×190,70×34.4232)y=∑i=170xi≈N(13300,82946.01)$

The probability that $y$ is greater than 17500is the area to the right of the normal curve. To find the area, first convert the value of sample mean $y>17500$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 17500is calculated as:

$P(Y>17500)=P(y−μσ>17500−13300288)=P(z>−14.58)=1−P(z≤−14.58)=1$

The area under the curve to the right of $P(z≤−14.58)$ is obtained as 0.000 from the standard normal table.

Therefore, the obtained probability is 1.

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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 5.1, Problem 20E

(a)

Section 1:

To determine

To find: Themean for the average number of friends per user for the provided sample.

(a)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is 190friends.

Explanation of Solution

The sample mean of average number of friends per user is calculated by the formula as:

$μx¯=∑i=1n=70x¯in=x¯1+x¯2+..+x¯69+x¯7070=190+190+...+19070=190$

It is provided that average number of friends on Facebook for eachuser is 190and the sample of70adult users is taken. Hence, the mean of the average number of friends per adult user is 190friends.

Section 2:

To determine

To find: The sample standard deviationfor the mean number of friends per adult user.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The sample standard deviation is $34.423$ .

Explanation of Solution

The standard deviation of sample means is calculated by the formula as:

$σx¯=σn=28870=34.423$

Hence, the sample standard deviation of mean of numbers friends per adult user is $34.423$ .

(b)

To determine

To find: The probability that the average number of friends for 70 Facebook users is greater than 250.

(b)

Expert Solution

Answer to Problem 20E

Solution: The probability is $0.0409$ .

Explanation of Solution

The probability that the average number of friends for 70Facebook users is greater than 250will be given by:

$P(x¯>250)$

The probability that $x¯$ is greater than 250is the area to the right of the normal curve. To find the area, first convert the value of sample mean $x¯>250$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 250is calculated as:

$P(x¯>250)=P(x¯−μσ/n>250−190288/70)=P(z>1.74)=1−P(z≤1.74)=1−0.9591=0.0409$

The area under the curveto the right of $P(z≤1.74)$ by using the standard normal table is obtained as $0.0409$ .

Therefore, the required probability that the sample of 70 Facebook users has minimum of 250 friends is $0.0409$ .

(c)

Section 1:

To determine

To find: The mean of total number of friends in the provided sample.

(c)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is27040.

Explanation of Solution

The sample mean of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample mean of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as::

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the mean of total number of friends in the sample is 13300.

Section 2:

To determine

To find: The standard deviation of total number of friends in the provided sample.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The standard deviation is 288.

Explanation of Solution

The sample standard deviation of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample standard deviation of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as:

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the standard deviation of total number of friends is calculated as:

$82946.01=288$

(d)

To determine

To find: The probability that the total number of friends for 70Facebook users is greater than 17500.

(d)

Expert Solution

Answer to Problem 20E

Solution: The probability is $1$ .

Explanation of Solution

The required probability that the mean of total number of friends of 70users is greater than 17500; that is the required probability will be given by:

$∑i=170xi≈N(70×190,70×34.4232)y=∑i=170xi≈N(13300,82946.01)$

The probability that $y$ is greater than 17500is the area to the right of the normal curve. To find the area, first convert the value of sample mean $y>17500$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 17500is calculated as:

$P(Y>17500)=P(y−μσ>17500−13300288)=P(z>−14.58)=1−P(z≤−14.58)=1$

The area under the curve to the right of $P(z≤−14.58)$ is obtained as 0.000 from the standard normal table.

Therefore, the obtained probability is 1.

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Answer 5

Chapter 5.1, Problem 20E

(a)

Section 1:

To determine

To find: Themean for the average number of friends per user for the provided sample.

(a)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is 190friends.

Explanation of Solution

The sample mean of average number of friends per user is calculated by the formula as:

$μx¯=∑i=1n=70x¯in=x¯1+x¯2+..+x¯69+x¯7070=190+190+...+19070=190$

It is provided that average number of friends on Facebook for eachuser is 190and the sample of70adult users is taken. Hence, the mean of the average number of friends per adult user is 190friends.

Section 2:

To determine

To find: The sample standard deviationfor the mean number of friends per adult user.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The sample standard deviation is $34.423$ .

Explanation of Solution

The standard deviation of sample means is calculated by the formula as:

$σx¯=σn=28870=34.423$

Hence, the sample standard deviation of mean of numbers friends per adult user is $34.423$ .

(b)

To determine

To find: The probability that the average number of friends for 70 Facebook users is greater than 250.

(b)

Expert Solution

Answer to Problem 20E

Solution: The probability is $0.0409$ .

Explanation of Solution

The probability that the average number of friends for 70Facebook users is greater than 250will be given by:

$P(x¯>250)$

The probability that $x¯$ is greater than 250is the area to the right of the normal curve. To find the area, first convert the value of sample mean $x¯>250$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 250is calculated as:

$P(x¯>250)=P(x¯−μσ/n>250−190288/70)=P(z>1.74)=1−P(z≤1.74)=1−0.9591=0.0409$

The area under the curveto the right of $P(z≤1.74)$ by using the standard normal table is obtained as $0.0409$ .

Therefore, the required probability that the sample of 70 Facebook users has minimum of 250 friends is $0.0409$ .

(c)

Section 1:

To determine

To find: The mean of total number of friends in the provided sample.

(c)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is27040.

Explanation of Solution

The sample mean of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample mean of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as::

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the mean of total number of friends in the sample is 13300.

Section 2:

To determine

To find: The standard deviation of total number of friends in the provided sample.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The standard deviation is 288.

Explanation of Solution

The sample standard deviation of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample standard deviation of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as:

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the standard deviation of total number of friends is calculated as:

$82946.01=288$

(d)

To determine

To find: The probability that the total number of friends for 70Facebook users is greater than 17500.

(d)

Expert Solution

Answer to Problem 20E

Solution: The probability is $1$ .

Explanation of Solution

The required probability that the mean of total number of friends of 70users is greater than 17500; that is the required probability will be given by:

$∑i=170xi≈N(70×190,70×34.4232)y=∑i=170xi≈N(13300,82946.01)$

The probability that $y$ is greater than 17500is the area to the right of the normal curve. To find the area, first convert the value of sample mean $y>17500$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 17500is calculated as:

$P(Y>17500)=P(y−μσ>17500−13300288)=P(z>−14.58)=1−P(z≤−14.58)=1$

The area under the curve to the right of $P(z≤−14.58)$ is obtained as 0.000 from the standard normal table.

Therefore, the obtained probability is 1.

Answer 6

Chapter 5.1, Problem 20E

(a)

Section 1:

To determine

To find: Themean for the average number of friends per user for the provided sample.

(a)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is 190friends.

Explanation of Solution

The sample mean of average number of friends per user is calculated by the formula as:

$μx¯=∑i=1n=70x¯in=x¯1+x¯2+..+x¯69+x¯7070=190+190+...+19070=190$

It is provided that average number of friends on Facebook for eachuser is 190and the sample of70adult users is taken. Hence, the mean of the average number of friends per adult user is 190friends.

Answer 7

Chapter 5.1, Problem 20E

(a)

Section 1:

To determine

To find: Themean for the average number of friends per user for the provided sample.

Answer 8

(a)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is 190friends.

Answer 9

(a)

Section 1:

Expert Solution

Answer 10

(a)

Section 1:

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The sample mean of average number of friends per user is calculated by the formula as:

$μx¯=∑i=1n=70x¯in=x¯1+x¯2+..+x¯69+x¯7070=190+190+...+19070=190$

It is provided that average number of friends on Facebook for eachuser is 190and the sample of70adult users is taken. Hence, the mean of the average number of friends per adult user is 190friends.

Answer 13

Section 2:

To determine

To find: The sample standard deviationfor the mean number of friends per adult user.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The sample standard deviation is $34.423$ .

Explanation of Solution

The standard deviation of sample means is calculated by the formula as:

$σx¯=σn=28870=34.423$

Hence, the sample standard deviation of mean of numbers friends per adult user is $34.423$ .

Answer 14

Section 2:

To determine

To find: The sample standard deviationfor the mean number of friends per adult user.

Answer 15

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The sample standard deviation is $34.423$ .

Answer 16

Section 2:

Expert Solution

Answer 17

Section 2:

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The standard deviation of sample means is calculated by the formula as:

$σx¯=σn=28870=34.423$

Hence, the sample standard deviation of mean of numbers friends per adult user is $34.423$ .

Answer 20

(b)

To determine

To find: The probability that the average number of friends for 70 Facebook users is greater than 250.

(b)

Expert Solution

Answer to Problem 20E

Solution: The probability is $0.0409$ .

Explanation of Solution

The probability that the average number of friends for 70Facebook users is greater than 250will be given by:

$P(x¯>250)$

The probability that $x¯$ is greater than 250is the area to the right of the normal curve. To find the area, first convert the value of sample mean $x¯>250$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 250is calculated as:

$P(x¯>250)=P(x¯−μσ/n>250−190288/70)=P(z>1.74)=1−P(z≤1.74)=1−0.9591=0.0409$

The area under the curveto the right of $P(z≤1.74)$ by using the standard normal table is obtained as $0.0409$ .

Therefore, the required probability that the sample of 70 Facebook users has minimum of 250 friends is $0.0409$ .

Answer 21

(b)

To determine

To find: The probability that the average number of friends for 70 Facebook users is greater than 250.

Answer 22

(b)

Expert Solution

Answer to Problem 20E

Solution: The probability is $0.0409$ .

Answer 23

(b)

Expert Solution

Answer 24

(b)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

The probability that the average number of friends for 70Facebook users is greater than 250will be given by:

$P(x¯>250)$

The probability that $x¯$ is greater than 250is the area to the right of the normal curve. To find the area, first convert the value of sample mean $x¯>250$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 250is calculated as:

$P(x¯>250)=P(x¯−μσ/n>250−190288/70)=P(z>1.74)=1−P(z≤1.74)=1−0.9591=0.0409$

The area under the curveto the right of $P(z≤1.74)$ by using the standard normal table is obtained as $0.0409$ .

Therefore, the required probability that the sample of 70 Facebook users has minimum of 250 friends is $0.0409$ .

Answer 27

(c)

Section 1:

To determine

To find: The mean of total number of friends in the provided sample.

(c)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is27040.

Explanation of Solution

The sample mean of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample mean of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as::

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the mean of total number of friends in the sample is 13300.

Answer 28

(c)

Section 1:

To determine

To find: The mean of total number of friends in the provided sample.

Answer 29

(c)

Section 1:

Expert Solution

Answer to Problem 20E

Solution: The mean is27040.

Answer 30

(c)

Section 1:

Expert Solution

Answer 31

(c)

Section 1:

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

The sample mean of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample mean of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as::

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the mean of total number of friends in the sample is 13300.

Answer 34

Section 2:

To determine

To find: The standard deviation of total number of friends in the provided sample.

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The standard deviation is 288.

Explanation of Solution

The sample standard deviation of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample standard deviation of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as:

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the standard deviation of total number of friends is calculated as:

$82946.01=288$

Answer 35

Section 2:

To determine

To find: The standard deviation of total number of friends in the provided sample.

Answer 36

Section 2:

Expert Solution

Answer to Problem 20E

Solution: The standard deviation is 288.

Answer 37

Section 2:

Expert Solution

Answer 38

Section 2:

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

The sample standard deviation of mean follow the approximate normal distribution with mean as 190and sample standard deviation as $34.423$ and the sample standard deviation of total number of friends is calculated as:

$x¯≈N(190,34.4232)$

And the total number of friends follows normal distribution with mean and variance as:

$∑i=170xi≈N(70×190,70×34.4232)∑i=170xi≈N(13300,82946.01)$

Hence, the standard deviation of total number of friends is calculated as:

$82946.01=288$

Answer 41

(d)

To determine

To find: The probability that the total number of friends for 70Facebook users is greater than 17500.

(d)

Expert Solution

Answer to Problem 20E

Solution: The probability is $1$ .

Explanation of Solution

The required probability that the mean of total number of friends of 70users is greater than 17500; that is the required probability will be given by:

$∑i=170xi≈N(70×190,70×34.4232)y=∑i=170xi≈N(13300,82946.01)$

The probability that $y$ is greater than 17500is the area to the right of the normal curve. To find the area, first convert the value of sample mean $y>17500$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 17500is calculated as:

$P(Y>17500)=P(y−μσ>17500−13300288)=P(z>−14.58)=1−P(z≤−14.58)=1$

The area under the curve to the right of $P(z≤−14.58)$ is obtained as 0.000 from the standard normal table.

Therefore, the obtained probability is 1.

Answer 42

(d)

To determine

To find: The probability that the total number of friends for 70Facebook users is greater than 17500.

Answer 43

(d)

Expert Solution

Answer to Problem 20E

Solution: The probability is $1$ .

Answer 44

(d)

Expert Solution

Answer 45

(d)

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

The required probability that the mean of total number of friends of 70users is greater than 17500; that is the required probability will be given by:

$∑i=170xi≈N(70×190,70×34.4232)y=∑i=170xi≈N(13300,82946.01)$

The probability that $y$ is greater than 17500is the area to the right of the normal curve. To find the area, first convert the value of sample mean $y>17500$ to a z-score and then obtain the area to the right of z-score from the standard normal table provided in the book.

The z-score for the value 17500is calculated as:

$P(Y>17500)=P(y−μσ>17500−13300288)=P(z>−14.58)=1−P(z≤−14.58)=1$

The area under the curve to the right of $P(z≤−14.58)$ is obtained as 0.000 from the standard normal table.

Therefore, the obtained probability is 1.

Answer 48

Ch. 5.1 - Prob. 1UYK Ch. 5.1 - Prob. 2UYK Ch. 5.1 - Prob. 3UYK Ch. 5.1 - Prob. 4UYK Ch. 5.1 - Prob. 5UYK Ch. 5.1 - Prob. 6UYK Ch. 5.1 - Prob. 7UYK Ch. 5.1 - Prob. 8UYK Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Themean for the average number of friends per user for the provided sample.

Concept explainers

Videos

To find: Themean for the average number of friends per user for the provided sample.

Answer to Problem 20E

Explanation of Solution

To find: The sample standard deviationfor the mean number of friends per adult user.

Answer to Problem 20E

Explanation of Solution

To find: The probability that the average number of friends for 70 Facebook users is greater than 250.

Answer to Problem 20E

Explanation of Solution

To find: The mean of total number of friends in the provided sample.

Answer to Problem 20E

Explanation of Solution

To find: The standard deviation of total number of friends in the provided sample.

Answer to Problem 20E

Explanation of Solution

To find: The probability that the total number of friends for 70Facebook users is greater than 17500.

Answer to Problem 20E

Explanation of Solution

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