Question

Suppose x has a distribution with μ = 40 and σ = 12. (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 = 40 and σ x = 0.8. Yes, the x distribution is normal with mean μ x = 40 and σ x = 12. Yes, the x distribution is normal with mean μ x = 40 and σ x = 3. No, the sample size is too small. Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (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 = 40 and σ x = 3. Yes, the x distribution is normal with mean μ x = 40 and σ x = 12. Yes, the x distribution is normal with mean μ x = 40 and σ x = 0.8.

Answer 1

a: no the sample size is too small

b: Yes, the distribution is normal with a mean of 40 and standard deviation of 12

Explanation:

a: If n < 30, we need to know that the sample is normally distributed or else we can't determine anything. When sample sized get very large, they usually resemble normally distributed data sets so we can still make conjectures even if the data isn't officially normally distributed

b: The question tells us that the sample is normally distributed, so even though n < 30, we can still make conjectures about the population