Question

In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find the energy consumption level for the 45th percentile. Group of answer choices

Answer 1

Answer: 1022.75 kWh.

Explanation:

Given: In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh.

i.e.
`\mu=1050\ kWh` and
`\sigma=218\ kWh`

Let X denote energy consumption levels for random single-family homes and x be the energy consumption level for the 45th percentile.

Then,
`P(X<x)=0.45`

From z-table,
`P(z<-0.125)=0.45`

Also,
`z=(x-\mu)/(\sigma)`

`\Rightarrow\ -0.125=(x-1050)/(218)\\\\\Rightarrow\ x=-0.125*218+1050=1022.75`

Hence, the energy consumption level for the 45th percentile is 1022.75 kWh.