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 μ = 1.5 and o= .2. Consider a random sample of 100 variable life insurance policies and let represent the mean ratio for the sample. a. Find E(T) and interpret its value.

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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 μ = 1.5 and o= .2. Consider a random sample of 100
variable life insurance policies and let a represent the mean
ratio for the sample.
a. Find E(T) and interpret its value.
b. Find Var(x).
c. Describe the shape of the sampling distribution of .
d. Find the z-score for the value = 1.52.
e. Find P(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
was 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 μ = 1.5 and o= .2. Consider a random sample of 100 variable life insurance policies and let a represent the mean ratio for the sample. a. Find E(T) and interpret its value. b. Find Var(x). c. Describe the shape of the sampling distribution of . d. Find the z-score for the value = 1.52. e. Find P(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 was not normally distributed? Explain.
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