A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.7 years, and standard deviation of 1.2 years. The 2% of items with the shortest lifespan will last less than how many years? Give your answer to one decimal p

Answer: 9.2 years

Step-by-step explanation:

Given the following:

Mean (m) = 11.7 years

Standard deviation (s) = 1.2 years

Recall the z-score formula:

Z = (x - m) / s

We can find the z-score by locating the value of 2% in the negative z-table, then solve for x.

2% = 0.02

0.02 falls most closely to 0.02018whuch is under - 2.05.

Using the z-score value in the formula above:

-2.05 = (x - 11.7) / 1.2

Cross multiply

(-2.05 * 1.2) = x - 11.7

-2.46 = x - 11.7

x = - 2.46 + 11.7

x = 9.24 years