MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Please do only part d and e

**5.28 Variable life insurance return rates** Refer to the *International Journal of Statistical Distributions* (Vol. 1, 2015) study of a variable life insurance policy, Exercise 4.97 (p. 239). Recall that a ratio (\(x\)) of the rates of return on the investment for two consecutive years was shown to have a normal distribution, with \(\mu = 1.5\) and \(\sigma = 0.2\). Consider a random sample of 100 variable life insurance policies and let \(\bar{x}\) represent the mean ratio for the sample. a. Find \(E(\bar{x})\) and interpret its value. b. Find \(\text{Var}(\bar{x})\). c. Describe the shape of the sampling distribution of \(\bar{x}\). d. Find the \(z\)-score for the value \(\bar{x} = 1.52\). e. Find \(P(\bar{x} > 1.52)\). f. Would your answers to parts a–e change if the rates (\(x\)) of return on the investment for two consecutive years were not normally distributed? Explain.
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Transcribed Image Text:**5.28 Variable life insurance return rates** Refer to the *International Journal of Statistical Distributions* (Vol. 1, 2015) study of a variable life insurance policy, Exercise 4.97 (p. 239). Recall that a ratio (\(x\)) of the rates of return on the investment for two consecutive years was shown to have a normal distribution, with \(\mu = 1.5\) and \(\sigma = 0.2\). Consider a random sample of 100 variable life insurance policies and let \(\bar{x}\) represent the mean ratio for the sample. a. Find \(E(\bar{x})\) and interpret its value. b. Find \(\text{Var}(\bar{x})\). c. Describe the shape of the sampling distribution of \(\bar{x}\). d. Find the \(z\)-score for the value \(\bar{x} = 1.52\). e. Find \(P(\bar{x} > 1.52)\). f. Would your answers to parts a–e change if the rates (\(x\)) of return on the investment for two consecutive years were not normally distributed? Explain.
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