(a) Explanation Given info: The data shows that the total cholesterol level of all men aged 20-34 follows a normal distribution with the mean μ = 182 milligrams per decilitre , standard deviation σ = 37 milligrams per decilitre , and the sample size ( n ) is 100. Calculation: Property : If X follows a normal distribution with mean μ and standard deviation σ , then, x ¯ with the sample size n follows a normal distribution with mean μ and standard deviation σ n . Let X be the cholesterol level of men aged 20-34. Here, X follows a normal distribution with mean μ = 182 mg/dL and standard deviation σ = 37 mg/dL . The sample size ( n ) is 100. Mean of the Sampling distribution of x ¯ : The sample mean x ¯ of sample size n has mean μ . Thus, the mean of the sampling distribution is 182 mg/dL. Standard deviation of the Sampling distribution of x ¯ : The standard deviation can be calculated by using the formula σ n . Substitute 37 for σ and 100 for n. σ n = 37 100 = 37 10 = 3.7 Thus, the standard deviation of x ¯ is 3.7 mg/dL. Hence, The sampling distribution of x ¯ follows a normal distribution with mean μ = 182 mg/dL and standard deviation σ n = 3 (b) To determine To find: The probability that x ¯ falls within ± 2 mg/dL .

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ISBN: 9781319057916

Author: Moore

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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 15.4, Problem 9AYK

(a)

To determine

To find: The sampling distribution of x¯ .

To calculate: The probability that x¯ takes a value between 180 and 184 mg/dL.

(b)

To determine

To find: The probability that x¯ falls within ±2 mg/dL .

Expert Solution & Answer

Chapter 15 Solutions

The Basic Practice of Statistics

Ch. 15.1 - Prob. 1AYK Ch. 15.1 - Prob. 2AYK Ch. 15.1 - Prob. 3AYK Ch. 15.2 - Prob. 4AYK Ch. 15.2 - Prob. 5AYK Ch. 15.3 - Prob. 6AYK Ch. 15.3 - Prob. 7AYK Ch. 15.4 - Prob. 8AYK Ch. 15.4 - Prob. 9AYK Ch. 15.4 - Prob. 10AYK

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