Normal DIstribution Question- Need Help

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.6 years, and standard deviation of 0.7 years.

The 10% of items with the shortest lifespan will last less than how many years?

Give your answer to one decimal place.

Answer 1

0.1 = P(z < x)

The z-score that corresponds with 10% probability is -2.33

z-score = (x - mean/ std)

so to find x, we equate

-2.33 = (x - 5.6)/0.7

x = 3.969 ~ 4.0