The shelf life of a battery produced by one major company is known to be normally distributed with a mean life of 9 years and a standard deviation of 0.2 years. What value of shelf life do 16% of the battery shelf lives fall below. What value of shelf life do 16% of the battery shelf lives fall above? Round your answer to one decimal place.

Answer: the value of shell life is 9.2 hours.

Step-by-step explanation:

Since the shelf life of a battery produced by one major company is known to be normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = shelf life of a batteries in years.

µ = mean shell life

σ = standard deviation

From the information given,

µ = 9 years

σ = 0.2 years

Looking at the normal distribution table, the z score corresponding to the p value of 16% (16/100 = 0.16) is - 0.9. Therefore

- 0.9 = (x - 9) / 0.2

0.2 * - 0.9 = x - 9

0.18 = x - 9

x = 0.18 + 9

x = 9.2