Question

Suppose x has a distribution with μ = 25 and σ = 2.

(a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?

Yes, the x distribution is normal with mean μ_x = 25 and σ_x = 0.5.No, the sample size is too small.     Yes, the x distribution is normal with mean μ_x = 25 and σ_x = 2.Yes, the x distribution is normal with mean μ_x = 25 and σ_x = 0.1.

(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?

No, the sample size is too small.

Yes, the x distribution is normal with mean μ_x = 25 and σ_x = 0.1.     

Yes, the x distribution is normal with mean μ_x = 25 and σ_x = 0.5.

Yes, the x distribution is normal with mean μ_x = 25 and σ_x = 2.

Find P(21 ≤ x ≤ 26). (Round your answer to four decimal places.)

Answer 1

(a) No, the sample size is too small

(b) Yes, Since X has normal distribution its sample will also have normal distribution.

If   Then sample also follows

So, sample has normal distribution with mean =25 , standard deviation == 2

where Z is a standard normal random variable.