Math Question on statistics

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.9 years, and standard deviation of 0.9 years.

The 2% of items with the shortest lifespan will last less than how many years?

Give your answer to one decimal place.

Answer 1

We will be using the equation:

z = (x - mean)/SD which is normally distributed with mean 0 and Standard deviation 1

x is the lifespan which has mean 5.9 and SD 0.9

we first need to find z corresponding to the 2nd percentile, which is -2.05

then we use above equation with z = -2.05, mean = 5.9 and SD = 0.9 to solve for x for the 2nd percentile:

-2.05 = (x - 5.9)/0.9

x = -2.05 * 0.9 + 5.9 = 4.055 years