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 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

We need to first calculate the standard error of the mean:
standard error of the mean = standard deviation / sqrt(sample size)
= 0.3 / sqrt(9)
= 0.1

Now we can calculate the z-score:
z = (sample mean - population mean) / standard error of the mean
= (29.95 - 30.05) / 0.1
= -1

Using a standard normal distribution table, we can find the probability that a z-score is less than -1, which is 0.1587. We want the probability that the sample mean is greater than 29.95, so we need to subtract this probability from 1:
P(sample mean > 29.95) = 1 - P(sample mean < 29.95)
= 1 - 0.1587
= 0.8413

Therefore, the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long is 0.8413 or choice A.

The Population of Lengths of Aluminum - Coated Steel Sheets