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Parts a, b, and d and explian how it was done. DON'T USE EXCEL, please do the work manually if you can

Parts a, b, and d and explian how it was done. DON'T USE EXCEL, please do the work manually if you can

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Parts a, b, and d and explian how it was done.

DON'T USE EXCEL, please do the work manually if you can 

**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 \(\overline{x}\) represent the mean ratio for the sample. a. **Find \(E(\overline{x})\)** and interpret its value. b. **Find \(Var(\overline{x})\).** c. **Describe the shape of the sampling distribution of \(\overline{x}\).** d. **Find the z-score for the value \(\overline{x} = 1.52\).** e. **Find \(P(\overline{x} > 1.52)\).** 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.**
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 \(\overline{x}\) represent the mean ratio for the sample. a. **Find \(E(\overline{x})\)** and interpret its value. b. **Find \(Var(\overline{x})\).** c. **Describe the shape of the sampling distribution of \(\overline{x}\).** d. **Find the z-score for the value \(\overline{x} = 1.52\).** e. **Find \(P(\overline{x} > 1.52)\).** 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.**
Expert Solution
Step 1

Given

The given data is as follows:

μ=1.5σ=0.2n=100

X~Nμ=1.5, σ2=0.22

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