Question

A simple random sample of size

nequals=3737

is obtained from a population with

muμequals=4343

and

sigmaσequals=77.

Does the population need to be normally distributed for the sampling distribution of

x overbarx

to be approximately normally​ distributed? Why? What is the sampling distribution of

x overbarx​?

Answer 1

Solution :

Given that ,

mean = = 43

standard deviation = = 7

n = 37

No because the Central Limit Theorem states that regardless of the shape of the underlying​ population, the sampling distribution of x overbar becomes approximately normal as the sample​ size, n, increases

The sampling distibution of is approximately normal,

=    = 43

= / n = 7 / 37 = 1.15