Question

A council provides information about life insurance in force per covered family in the hand book. Assume that the standard deviation of life insurance in force is $50,900.

a. Determine the probability that the sampling error made in estimating the population mean life insurance in force by that of a sample of 500 covered families will be $2000 or less.

b. Must you assume that life-insurance amounts are normally distributed in order to answer part (a)? What if the sample size is 20 instead of 500?

c. Repeat part (a) for a sample of size 5000.

Answer 1

Central Limit theorem is Regardless the distribution of the variable under consideration the variable is approximately normal for reasonably large sample size and the approximation becomes better when increase in sample size.

Sampling of the distribution of mean and sample size 5000 is approximately normal with mean Ux = u and sd = $719.83