Question

A random sample is drawn from a normally distributed population with mean μ = 30 and standard deviation σ = 2.3. [You may find it useful to reference the z table.]

a. Are the sampling distribution of the sample mean with n = 35 and n = 76 normally distributed?

• Yes, both the sample means will have a normal distribution.

• No, both the sample means will not have a normal distribution.

• No, only the sample mean with n = 35 will have a normal distribution.

• No, only the sample mean with n = 76 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 30.7 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

n	Probability
35
76

Answer 1

(a) Ans : Yes, both the sample means will have a normal distribution.

(b)