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FromTheMoon [43]
3 years ago
6

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
Mathematics
1 answer:
Andrej [43]3 years ago
8 0

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.

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