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. What is the probability that a sheet selected at random will be less than 29.75 inches long

Answer 1

6.68% or 0.0668

Explanation:

Mean sheet length (μ) = 30.05 inches

Standard deviation (σ) = 0.2 inches

In a normal distribution, for any length X, the z-score is determined by the following expression:

`z=(X-\mu)/(\sigma)`

For X = 29.75, the z-score is:

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

A z-score of -1.5 corresponds to the 6.68th percentile of a normal distribution.

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