The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.What is the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long?
A).0668
B).9332
C).0014
D).4404

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the distribution of sample means. The distribution of sample means will also be normally distributed with a mean of μ (30.05) and a standard deviation of σ/√n (0.2/√4 = 0.1).

We need to find the probability that a sample of 4 sheets will have a sample mean of less than 29.9 inches long.

z = (x̄ - μ) / (σ/√n) 
z = (29.9 - 30.05) / (0.1) 
z = -1.5

Using the standard normal distribution table, we can find the area to the left of z = -1.5, which is 0.0668. Therefore, the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long is 0.0668.

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