Question

Please show complete work and all calculations

Using the following information for a population of data points X :

n=30 =5   ² =4 ( population variance)

A) What is the distribution of the population of sample means?

B) Find the probability that the sample mean is less than 4 ?

Answer 1

Solution:

Given:

n =30

Part A) What is the distribution of the population of sample means?

Since sample size is n = 30  is large , we can use Central limit theorem which states that for large sample size n ,
the distribution of the population of sample means is approximately normal with mean of sample means:

and standard deviation of sample means is:

Part B) Find the probability that the sample mean is less than 4 ?

Find z score for

thus we get:

Look in z table for z = -2.7 and 0.04 and find corresponding area.

P( Z<-2.74) = 0.0031

thus