The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.3 inches.What is the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long?
A).8413
B).6293
C).3707
D).1587

Question

Quizplus · Accepted Answer

The sample mean has a normal distribution with the same mean (30.05 inches) and a standard deviation of 0.3/sqrt(9) = 0.1 inches. The Z-score for 29.95 is (29.95 - 30.05) / 0.1 = -1. The probability of Z being greater than -1 is 0.8413.

The Population of Lengths of Aluminum-Coated Steel Sheets Is Normally