A sociologist is studying the number of years of education of students whose mothers have bachelor's degrees or higher. The data is normally distributed with a population mean of 14.5 years and a population standard deviation of 2.5 years. If a sample of 55 students is selected at random from the population, select the mean and standard deviation of the sampling distribution below. a. σi= 0.05 years
b. σi= 2.5 years
c. σi= 0.34 years
d. µ= 14.5 years

The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

Population:

Sample:

55 students, so

Then

The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.

doubled

step-by-step explanation: