The shape of the distribution of the bone density test scores.

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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, Problem 1CQQ

To determine

To sketch: The shape of the distribution of the bone density test scores.

Expert Solution & Answer

Explanation of Solution

Given information:

It is given that the bone density test scores follow the normal distribution with a mean of 0 and a standard deviation of 1.

The normal distribution is a bell-shaped distribution. The mean value of 0 is the center of bell-shaped distribution and almost the entire area under the curve is located between -3 to 3.

Graph:

First draw a horizontal axis and mark it from -3 to 3. Then draw a bell-shape curve from -3 to 3 and put the value 0 at the center.

The obtained shape of the distribution of the given scores is given below:

EBK ELEMENTARY STATISTICS USING EXCEL, Chapter 6, Problem 1CQQ

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iid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²

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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, Problem 1CQQ

To determine

To sketch: The shape of the distribution of the bone density test scores.

Expert Solution & Answer

Explanation of Solution

Given information:

It is given that the bone density test scores follow the normal distribution with a mean of 0 and a standard deviation of 1.

The normal distribution is a bell-shaped distribution. The mean value of 0 is the center of bell-shaped distribution and almost the entire area under the curve is located between -3 to 3.

Graph:

First draw a horizontal axis and mark it from -3 to 3. Then draw a bell-shape curve from -3 to 3 and put the value 0 at the center.

The obtained shape of the distribution of the given scores is given below:

EBK ELEMENTARY STATISTICS USING EXCEL, Chapter 6, Problem 1CQQ

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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 6, Problem 1CQQ

To determine

To sketch: The shape of the distribution of the bone density test scores.

Expert Solution & Answer

Explanation of Solution

Given information:

It is given that the bone density test scores follow the normal distribution with a mean of 0 and a standard deviation of 1.

The normal distribution is a bell-shaped distribution. The mean value of 0 is the center of bell-shaped distribution and almost the entire area under the curve is located between -3 to 3.

Graph:

First draw a horizontal axis and mark it from -3 to 3. Then draw a bell-shape curve from -3 to 3 and put the value 0 at the center.

The obtained shape of the distribution of the given scores is given below:

EBK ELEMENTARY STATISTICS USING EXCEL, Chapter 6, Problem 1CQQ

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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 6, Problem 1CQQ

To determine

To sketch: The shape of the distribution of the bone density test scores.

Expert Solution & Answer

Explanation of Solution

Given information:

It is given that the bone density test scores follow the normal distribution with a mean of 0 and a standard deviation of 1.

The normal distribution is a bell-shaped distribution. The mean value of 0 is the center of bell-shaped distribution and almost the entire area under the curve is located between -3 to 3.

Graph:

First draw a horizontal axis and mark it from -3 to 3. Then draw a bell-shape curve from -3 to 3 and put the value 0 at the center.

The obtained shape of the distribution of the given scores is given below:

EBK ELEMENTARY STATISTICS USING EXCEL, Chapter 6, Problem 1CQQ

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Answer 5

Chapter 6, Problem 1CQQ

To determine

To sketch: The shape of the distribution of the bone density test scores.

Expert Solution & Answer

Explanation of Solution

Given information:

It is given that the bone density test scores follow the normal distribution with a mean of 0 and a standard deviation of 1.

The normal distribution is a bell-shaped distribution. The mean value of 0 is the center of bell-shaped distribution and almost the entire area under the curve is located between -3 to 3.

Graph:

First draw a horizontal axis and mark it from -3 to 3. Then draw a bell-shape curve from -3 to 3 and put the value 0 at the center.

The obtained shape of the distribution of the given scores is given below:

EBK ELEMENTARY STATISTICS USING EXCEL, Chapter 6, Problem 1CQQ

Answer 6

Chapter 6, Problem 1CQQ

To determine

To sketch: The shape of the distribution of the bone density test scores.

Expert Solution & Answer

Explanation of Solution

Given information:

It is given that the bone density test scores follow the normal distribution with a mean of 0 and a standard deviation of 1.

The normal distribution is a bell-shaped distribution. The mean value of 0 is the center of bell-shaped distribution and almost the entire area under the curve is located between -3 to 3.

Graph:

First draw a horizontal axis and mark it from -3 to 3. Then draw a bell-shape curve from -3 to 3 and put the value 0 at the center.

The obtained shape of the distribution of the given scores is given below:

EBK ELEMENTARY STATISTICS USING EXCEL, Chapter 6, Problem 1CQQ

Answer 7

Chapter 6, Problem 1CQQ

To determine

To sketch: The shape of the distribution of the bone density test scores.

Answer 8

Expert Solution & Answer

Explanation of Solution

Given information:

It is given that the bone density test scores follow the normal distribution with a mean of 0 and a standard deviation of 1.

The normal distribution is a bell-shaped distribution. The mean value of 0 is the center of bell-shaped distribution and almost the entire area under the curve is located between -3 to 3.

Graph:

First draw a horizontal axis and mark it from -3 to 3. Then draw a bell-shape curve from -3 to 3 and put the value 0 at the center.

The obtained shape of the distribution of the given scores is given below:

EBK ELEMENTARY STATISTICS USING EXCEL, Chapter 6, Problem 1CQQ