A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is greater than 18 is ________.
A) 0.1587
B) 0.4325
C) 0.5675
D) 0.8413

Question

Quizplus · Accepted Answer

The sample mean follows a normal distribution with mean µ = 17 and standard deviation σ/√n = 6/√36 = 1. The z-score for a sample mean of 18 is (18-17)/1 = 1. The probability that the sample mean is greater than 18 corresponds to the area to the right of z = 1, which is 0.1587.

A Random Sample of Size 36 Is Taken from a Population