Which describes the correlation shown in the scatterplot?

On a graph, points are grouped closely together and increase.
There is a positive correlation in the data set.
There is a negative correlation in the data set.
There is no correlation in the data set.
More points are needed to determine the correlation.

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.