According to a recent survey, the population distribution of number of years of education for self-employed individuals in a certain region has a mean of 15.1 and a standard deviation of 4.8.

a. identify the random variable x whose distribution is described here.
b. find the mean and the standard deviation of the sampling distribution of x overbar for a random sample of size 36. interpret them.
c. repeat (b) for nequals144. describe the effect of increasing n.

a)  X that is a distribution of number of years of education for self-employed individuals.

b) Mean = 15.1, Standard Deviation = 0.8

c) Mean = 15.1, Standard Deviation = 0.4

Step-by-step explanation:

We are given the following in the question:

The population distribution of number of years of education for self-employed individuals in a certain region has a mean of 15.1 and a standard deviation of 4.8

a) The random variable is X that is a distribution of number of years of education for self-employed individuals.

b) According to central limit theorem, as the sample size increases the distribution of means approaches a normal distribution.

Thus, has a normal distribution with

c) n = 144

has a normal distribution with

By increasing n, the standard deviation for distribution of mean reduced  by one half. Therefore, we see that quadrupling the sample size will reduce the standard deviation by one half.

a

step-by-step explanation: