Question

A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $91 and a standard deviation of $8. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $83?

Answer 1

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

Explanation:

If the distribution of the monthly utility bill for gas or electric energy can be considered mound-shaped and symmetric, we can use the standard normal distribution table to find the percentage of homes that have a monthly utility bill of more than $83.

To use the standard normal distribution table, we need to standardize the variable by subtracting the mean and dividing by the standard deviation:

(83 - 91) / 8 = -0.875

This means that a monthly utility bill of $83 is 0.875 standard deviations below the mean.

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.