Data Set 8-9: A population mean (µ) of 4 and a standard deviation ($\sigma$) of 2. (Carry 3 or 4 decimal places in your calculations.)
-What is the probability that a random sample with N = 7 from Data Set 8-9 would have a mean of 3 or less?
A) .4998
B) .4066
C) .3085
D) 19.15
E) .0934
F) .0002

Question

Quizplus · Accepted Answer

To find the probability that a sample mean is 3 or less, use the standard normal distribution. The standard error (SE) is $\sigma/\sqrt{N} = 2/\sqrt{7} \approx 0.7559$. The z-score is $(3 - 4)/0.7559 \approx -1.3229$. Using the z-table, the probability corresponding to a z-score of -1.3229 is approximately 0.0934.

Data Set 8-9: a Population Mean (µ) of 4 and a Standard