Solve the problem.
-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 P45, which is the consumption level separating the bottom 45% from the top 55%.
A)1148.1
B)1021.7
C)1078.3
D)1087.8

Question

Quizplus · Accepted Answer

P45 corresponds to the 45th percentile of the distribution. To find this, we use the Z-score formula for a percentile in a normal distribution, which is Z = (X - μ) / σ, where X is the value we're looking for, μ is the mean, and σ is the standard deviation. However, since we're given the percentile (45th), we first find the Z-score corresponding to the 45th percentile from a Z-table or using a calculator. The Z-score for the 45th percentile is approximately -0.125. Plugging this into the formula and solving for X gives us X = Zσ + μ. Substituting the given values (μ = 1050, σ = 218, Z ≈ -0.125) results in X ≈ 1021.7, which corresponds to option B.

Solve the Problem. -In One Region, the September Energy Consumption Levels for Single-Family