A random sample of n = 16 scores is selected from a normal distribution with μ = 500 and σ = 200.For this sample,which of the following is true?
A)p(402

Question

A random sample of n = 16 scores is selected from a normal distribution with μ = 500 and σ = 200.For this sample,which of the following is true?
A)p(402 < M < 598) = 0.95
B)p(425 < M < 575) = 0.95
C)p(450 < M < 550) = 0.95
D)p(490 < M < 510) = 0.95

Quizplus · Accepted Answer

The correct choice is based on the calculation of the probability that the sample mean (M) falls within a certain range, using the standard error of the mean (σM = σ / √n) and the properties of the normal distribution. Given σ = 200 and n = 16, the standard error σM = 200 / √16 = 50. The z-score for a 95% confidence interval around the mean (μ = 500) in a standard normal distribution is approximately ±1.96. Thus, the range for M is μ ± 1.96*σM = 500 ± 1.96*50 = 500 ± 98, which gives the range from 402 to 598, making option A correct.

A Random Sample of N = 16 Scores Is Selected