## 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.

Question

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. A sample of four metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 inches long

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2 hours 2021-09-13T15:33:42+00:00 1 Answer 0

Probability that the average length of a sheet is between 30.25 and 30.35 inches long is 0.0214 .

Step-by-step explanation:

We are given that 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.

Also, a sample of four metal sheets is randomly selected from a batch.

Let X bar = Average length of a sheet

The z score probability distribution for average length is given by;

Z = ~ N(0,1)

where, = population mean = 30.05 inches = standard deviation = 0.2 inches

n = sample of sheets = 4

So, Probability that average length of a sheet is between 30.25 and 30.35 inches long is given by = P(30.25 inches < X bar < 30.35 inches)

P(30.25 inches < X bar < 30.35 inches)  = P(X bar < 30.35) – P(X bar <= 30.25)

P(X bar < 30.35) = P( < ) = P(Z < 3) = 0.99865

P(X bar <= 30.25) = P( <= ) = P(Z <= 2) = 0.97725

Therefore, P(30.25 inches < X bar < 30.35 inches)  = 0.99865 – 0.97725

= 0.0214