Refer to the International Journal of Statistical Distributions (Vol. 1, 2015) study of a variable life insurance policy, Exercise 4.97 (p. 238). 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 μ = 1.5 and σ = .2. Consider a random sample of 100 variable life insurance policies and let x̅ represent the mean ratio for the sample.
a. Find E(x̅) and interpret its value.
b. Find Var(x̅).
c. Describe the shape of the sampling distribution of x̅.
d. Find the z-score for the value x̅ = 1.52.
e. Find P(x̅ > 1.52).
f. Would your answers to parts a- e change if the rates (x) of return on the investment for two consecutive years was not normally distributed? Explain.