A random sample of n = 9 scores is selected from a normal distribution with μ = 80 and σ = 12.What is the probability that the sample mean will be between 76 and 84?
A)0.9974
B)0.6426
C)0.3830
D)0.2586

Question

Quizplus · Accepted Answer

The standard error of the mean is σ/√n = 12/√9 = 4. The z-scores for 76 and 84 are (76-80)/4 = -1 and (84-80)/4 = 1, respectively. The probability of a z-score between -1 and 1 is approximately 0.6826. However, since the options provided do not match this exactly, the closest option is 0.6426.

A Random Sample of N = 9 Scores Is Selected