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 between 15 and 18 is _______.
A) 0.0228
B) 0.8185
C) 0.8413
D) 0.8641

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-scores for 15 and 18 are (15-17)/1 = -2 and (18-17)/1 = 1, respectively. The probability of a z-score between -2 and 1 is approximately 0.8185.

A Random Sample of Size 36 Is Taken from a Population