A random sample of n = 25 individuals is drawn from a population with a μ = 63 and a σ = 9. The probability is .1000 that the mean of the sample will be above what value?
A) -1.28
B) +1.28
C) 65.3
D) 60.70

Question

Quizplus · Accepted Answer

First, we need to find the z-score that corresponds to a probability of .1000 in the upper tail of the standard normal distribution. Using a standard normal distribution table or calculator, this z-score is approximately 1.28.

Next, we use the formula for the standard error of the mean:

SE = σ/√n

SE = 9/√25

SE = 1.8

Finally, we use the formula for the sample mean:

M = μ + z*SE

M = 63 + 1.28*1.8

M = 65.304

So the probability is .1000 that the mean of the sample will be above 65.304. Therefore, the best choice is C.

A Random Sample of N = 25 Individuals Is Drawn