A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.4 years, and standard deviation of 0.7 years. the 8% of items with the shortest lifespan will last less than how many years? give your answer to one decimal place.

To solve this problem, we make use of the z statistic. We are to look for the bottom 8% who has the shortest lifespan, this is equivalent to a proportion of P = 0.08. Using the standard distribution tables for z, the value of z corresponding to this P value is:

z = - 1.4

Now given the z and standard deviation s and the mean u, we can calculate for the number of years of the shortest lifespan:

x = z s + u

x = - 1.4 (0.7) + 2.4

x = - 0.98 + 2.4

x = 1.42 years

Therefore the life span is less than about 1.42 years