Question

A random sample is selected from a population with mean μ = 99 and standard deviation σ = 10. For which of the sample sizes would it be reasonable to think that the x sampling distribution is approximately normal in shape? (Select all that apply.)

a. n = 9
b. n = 19
c. n = 40
d. n = 70
e. n = 140
f. n = 560

Answer 1

Sample sizes n = 40, n = 70, n = 140, and n = 560 are large enough for the sampling distribution of the sample mean to be approximately normal according to the Central Limit Theorem.

Step-by-step explanation:

The question asks for which sample sizes it would be reasonable to assume that the sampling distribution of the sample mean is approximately normal. According to the Central Limit Theorem (CLT), the sampling distribution of the sample mean will be approximately normal if the sample size is large enough, even if the population distribution is not normal. The rule of thumb is that a sample size of 30 or more is generally considered sufficient for the CLT to hold.

• n = 9: Might not be sufficiently large for the sampling distribution to be approximately normal.
• n = 19: Closer to 30, but still may not be large enough for the sampling distribution to be normal.
• n = 40: Usually considered large enough for the sampling distribution to be approximately normal.
• n = 70: Sufficiently large.
• n = 140: Sufficiently large.
• n = 560: Well above 30, highly likely to be normal.

Therefore, sample sizes n = 40, n = 70, n = 140, and n = 560 would be the ones where it's reasonable to expect the sampling distribution of the sample mean to approximate normality.