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 sheet selected at random will be less than 29.75 inches long?
A).8944
B).1056
C).9332
D).0668

Question

Quizplus · Accepted Answer

We need to find the probability that a randomly selected sheet will be less than 29.75 inches long. We can use the standard normal distribution to find this probability.

First, we need to standardize the value of 29.75 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (29.75 - 30.05) / 0.2 = -1.5

Now, we need to find the probability that z is less than -1.5. We can use a standard normal distribution table or calculator to find this probability.

From the table, we find that the probability of z being less than -1.5 is approximately 0.0668.

Therefore, the probability that a sheet selected at random will be less than 29.75 inches long is approximately 0.0668, or 6.68%.

The closest answer choice is D) 0.0668, which is the correct answer.

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