Answered: Let X denote the amount of time a…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 36E

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Question

Let X denote the amount of time a randomly selected customer spends on hold with some insurance company. Suppose X follows a distribution with a mean of 8 hours and a variance of 16 hours. The population density curve for X is shown below.

a) Is the population normally distributed? Explain.

b) If you randomly pick twenty-five customers, describe the sampling distribution of the average time spent in the store; provide the mean, standard deviation, and shape.

c) If you randomly pick one hundred customers, describe the sampling distribution of the average time spent in the store; provide the mean, standard deviation, and shape.

Value of density curve
0.10
0.08
0.06
0.04
0.02
0.00
Population Distribution for Time spent on hold
5
10
15
Time Spent on hold (hours)
20
25
30

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.

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