The sampling distribution of the sample means with n = 40 and the necessary condition to apply the central limit theorem.

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Answer 1

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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 8, Problem 16E

(a)

To determine

To describe: The sampling distribution of the sample means with n=40 and the necessary condition to apply the central limit theorem.

(b)

To determine

To find: The standard error of the sampling distribution of the sample means.

(c)

To determine

To find: The probability that a sample mean is less than 74.

(d)

To determine

To find: The probability that a sample mean is between 74 and 76.

(e)

To determine

To find: The probability that a sample mean is between 76 and 77.

(f)

To determine

To find: The probability that the sampling error x¯−μ would be 1.50 or less.

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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 8, Problem 16E

(a)

To determine

To describe: The sampling distribution of the sample means with n=40 and the necessary condition to apply the central limit theorem.

(b)

To determine

To find: The standard error of the sampling distribution of the sample means.

(c)

To determine

To find: The probability that a sample mean is less than 74.

(d)

To determine

To find: The probability that a sample mean is between 74 and 76.

(e)

To determine

To find: The probability that a sample mean is between 76 and 77.

(f)

To determine

To find: The probability that the sampling error x¯−μ would be 1.50 or less.

Expert Solution & Answer

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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 8, Problem 16E

(a)

To determine

To describe: The sampling distribution of the sample means with n=40 and the necessary condition to apply the central limit theorem.

(b)

To determine

To find: The standard error of the sampling distribution of the sample means.

(c)

To determine

To find: The probability that a sample mean is less than 74.

(d)

To determine

To find: The probability that a sample mean is between 74 and 76.

(e)

To determine

To find: The probability that a sample mean is between 76 and 77.

(f)

To determine

To find: The probability that the sampling error x¯−μ would be 1.50 or less.

Expert Solution & Answer

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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 8, Problem 16E

(a)

To determine

To describe: The sampling distribution of the sample means with n=40 and the necessary condition to apply the central limit theorem.

(b)

To determine

To find: The standard error of the sampling distribution of the sample means.

(c)

To determine

To find: The probability that a sample mean is less than 74.

(d)

To determine

To find: The probability that a sample mean is between 74 and 76.

(e)

To determine

To find: The probability that a sample mean is between 76 and 77.

(f)

To determine

To find: The probability that the sampling error x¯−μ would be 1.50 or less.

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Answer 5

Chapter 8, Problem 16E

(a)

To determine

To describe: The sampling distribution of the sample means with n=40 and the necessary condition to apply the central limit theorem.

(b)

To determine

To find: The standard error of the sampling distribution of the sample means.

(c)

To determine

To find: The probability that a sample mean is less than 74.

(d)

To determine

To find: The probability that a sample mean is between 74 and 76.

(e)

To determine

To find: The probability that a sample mean is between 76 and 77.

(f)

To determine

To find: The probability that the sampling error x¯−μ would be 1.50 or less.

Answer 6

Chapter 8, Problem 16E

(a)

To determine

To describe: The sampling distribution of the sample means with n=40 and the necessary condition to apply the central limit theorem.

Answer 7

Chapter 8, Problem 16E

(a)

To determine

To describe: The sampling distribution of the sample means with n=40 and the necessary condition to apply the central limit theorem.

Answer 8

(b)

To determine

To find: The standard error of the sampling distribution of the sample means.

Answer 9

(b)

To determine

To find: The standard error of the sampling distribution of the sample means.

Answer 10

(c)

To determine

To find: The probability that a sample mean is less than 74.

Answer 11

(c)

To determine

To find: The probability that a sample mean is less than 74.

Answer 12

(d)

To determine

To find: The probability that a sample mean is between 74 and 76.

Answer 13

(d)

To determine

To find: The probability that a sample mean is between 74 and 76.

Answer 14

(e)

To determine

To find: The probability that a sample mean is between 76 and 77.

Answer 15

(e)

To determine

To find: The probability that a sample mean is between 76 and 77.

Answer 16

(f)

To determine

To find: The probability that the sampling error x¯−μ would be 1.50 or less.

Answer 17

(f)

To determine

To find: The probability that the sampling error x¯−μ would be 1.50 or less.

Answer 18

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Answer 19

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Answer 20

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Answer 21

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The sampling distribution of the sample means with n = 40 and the necessary condition to apply the central limit theorem.

To describe: The sampling distribution of the sample means with n=40 and the necessary condition to apply the central limit theorem.

To find: The standard error of the sampling distribution of the sample means.

To find: The probability that a sample mean is less than 74.

To find: The probability that a sample mean is between 74 and 76.

To find: The probability that a sample mean is between 76 and 77.

To find: The probability that the sampling error x¯−μ would be 1.50 or less.

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