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.

Step-by-step 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, $P(X$

From z-table, $P(z$

Also, $z=\dfrac{x-\mu}{\sigma}$

$\Rightarrow\ -0.125=\dfrac{x-1050}{218}\\\\\Rightarrow\ x=-0.125\times218+1050=1022.75$

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