Question

A random sample drawn from a population with mean μ= 66 and standard deviation σ= 6.

Required:
a. Comment on the sampling distribution of the sample mean with n = 16 and n = 36.
b. Can you use standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 for both sample sizes?
c. Report the probability if you answered yes to the previous question for either sample size.

Answer 1

In step by step explanation

Explanation:

a) Normal distribution N( 0, 1 )

If the sample size is equal n = 16 we have to use t-student distribution since n < 30.

In the case n = 36 we should use normal distribution (z tables)

b) We can´t use the standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 in the first case n < 30 .

We can calculate that probability in the case of the second sample