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?

Question

Mathematics

Kobe Villarreal

17 February, 13:16

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?

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Answers (1)

Know the Answer?

Lia Rubio · Answer 1

0.5358

Step-by-step 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 ...