Question

Electricity bills in a certain city have mean $ 106.27 . Assume the bills are normally distributed with standard deviation $ 17.15 . Find the value that separates the lower 40 % of the bills from the rest.

Write only a number as your answer. Round to two decimal places (for example: 42.81). Do not write any units.

Answer 1

Explanation:

To find the value that separates the lower 40% of the bills from the rest, we need to find the z-score corresponding to the 40th percentile of the standard normal distribution, and then use this z-score to find the corresponding value in the distribution of electricity bills.

Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 40th percentile is approximately -0.25.

To find the corresponding value in the distribution of electricity bills, we can use the formula:

z = (x - mu) / sigma

where z is the z-score, x is the corresponding value in the distribution, mu is the mean, and sigma is the standard deviation.

Rearranging this formula to solve for x, we get:

x = mu + z * sigma

Substituting the given values, we get:

x = 106.27 + (-0.25) * 17.15

x = 101.63

Therefore, the value that separates the lower 40% of the electricity bills from the rest is approximately $101.63.