A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.7 years, and standard deviation of 2.5 years. if you randomly purchase one item, what is the probability it will last longer than 8 years?

Question

Mathematics

Anabelle

21 June, 16:16

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.7 years, and standard deviation of 2.5 years. if you randomly purchase one item, what is the probability it will last longer than 8 years?

+2

Answers (1)

Know the Answer?

Nina Wheeler · Answer 1

First let us calculate for the z score using the formula:

z = (x - u) / s

where x = 8, u is the mean = 12.7 years, s is the standard deviation

z = (8 - 12.7) / 2.5

z = - 1.88

From the standard probability tables, the p value at z = - 1.88 is:

P = 0.0301 = 3.01%