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 45th percentile.

Answer 1

To find the 45th percentile of the September energy consumption levels for single-family homes, use the z-score formula with the mean and standard deviation. The 45th percentile is approximately 2073.468 kWh.

Step-by-step explanation:

To find the 45th percentile of the September energy consumption levels for single-family homes in a region, we need to use the normal distribution. The mean is 1050 kWh and the standard deviation is 218 kWh. First, we find the z-score corresponding to the 45th percentile using the z-table or a calculator. The z-score is approximately -0.126. Next, we use the z-score formula: z = (x - mean) / standard deviation. We rearrange the formula to solve for x, the energy consumption level: x = (z * standard deviation) + mean. Plugging in the values, we get x = (-0.126 * 218) + 1050. That gives us x = 1050 - 27.468 + 1050 = 2073.468. So, the 45th percentile of energy consumption is approximately 2073.468 kWh.