A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.1 years, and standard deviation of 0.6 years.

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.1 years, and standard deviation of 0.6 years.

The 6% of items with the shortest lifespan will last less than how many years?

Answer 1

z = (x - mean)/std dev, where x = lifespan, mean = 4.1 and std dev = 0.6

0.06 corresponds to -1.555 z, so

-1.555 = (x - 4.1)/0.6

x = -1.555(0.6) + 4.1 = 3.167 years