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.

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

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2