a . Explanation Given info: The annual salaries follow normal distribution with mean $61,000 and standard deviation $11,000. The sample of size is 45. Calculation: The random variable x represents annual salaries. The notation x ¯ represents mean annual salaries. The mean and standard deviation of the sampling distribution of sample means is represented by μ x ¯ and σ x ¯ , respectively. The distribution of sample means is normal with the parameters μ x ¯ and σ x ¯ by using central limit theorem. The mean of the sampling distribution of sample means is, μ x ¯ = μ . Here, the population mean is, μ = $ 60 , 000 . Therefore, the sampling distribution of the sample mean is, μ x ¯ = $ 60 , 000 . The formula to find the standard deviation of the sample means ( σ x ¯ ) is, σ x ¯ = σ n Substitute 11,000 for σ and 45 for n σ x ¯ = 11 , 000 45 = 11 , 000 6 b. To determine To obtain: The probability that the mean annual salary of the samples is more than $63,000. To interpret: The results of (a) and (b).

Elementary Statistics Plus MyLab Statistics with Pearson eText -- Access Card Package (7th Edition) (What's New in Statistics)

7th Edition

ISBN: 9780134684901

Author: Ron Larson, Betsy Farber

Publisher: PEARSON

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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 5, Problem 5.4.59RE

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To obtain: The probability that the mean annual salary of the samples is less than $60,000.

To determine

To obtain: The probability that the mean annual salary of the samples is more than $63,000.

To interpret: The results of (a) and (b).

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Chapter 5, Problem 5.4.58RE

Chapter 5, Problem 5.4.60RE

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Chapter 5 Solutions

Elementary Statistics Plus MyLab Statistics with Pearson eText -- Access Card Package (7th Edition) (What's New in Statistics)

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To obtain: The probability that the mean annual salary of the samples is less than $60,000.

Solution Summary: The author calculates the probability that the mean annual salary of the samples is less than 60,000 by using central limit theorem.

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To obtain: The probability that the mean annual salary of the samples is less than $60,000.

To obtain: The probability that the mean annual salary of the samples is more than $63,000. To interpret: The results of (a) and (b).

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Chapter 5 Solutions

To obtain: The probability that the mean annual salary of the samples is more than $63,000.

To interpret: The results of (a) and (b).