Data Set 8-7: A population with a mean (µ) of 10 and a standard deviation ($\sigma$) of 1. (Carry 3 or 4 decimals in your calculations.)
-What is the probability that a random sample with N = 7 from Data Set 8-7 would have a mean of 9 or smaller?
A) .0557
B) .1587
C) .3414
D) .4443
E) .4960
F) 0.0040

Question

Quizplus · Accepted Answer

The standard error of the mean (SEM) is $\sigma/\sqrt{N} = 1/\sqrt{7} \approx 0.377$. The z-score for a sample mean of 9 is $(9 - 10)/0.377 \approx -2.652$. Using the standard normal distribution table, the probability of a z-score of -2.652 or smaller is approximately 0.0040.

Data Set 8-7: a Population with a Mean (µ) of 10