Question

A manufacturer knows that their items have a normally distributed length, with a mean of 13.2 inches, and standard deviation of 2.2 inches. If one item is chosen at random, what is the probability that it is less than 13.4 inches long?

Answer 1

0.5358

Explanation:

Given

mean = μ = 13.2 inches

and

SD = σ = 2.2 inches

We have to find z-score for the given value 13.4 first

z-score = (x-μ)/σ

= (13.4-13.2)/2.2

=0.2/2.2

=0.0909

We have to find the area to the left of given z-score

The area to the left is 0.5358

So, the probability of choosing an item with length less than 13.4 is 0.5358 ..