Question

statistics informed decisions 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 $143 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 $135?

Answer 1

84.13% of homes will have a monthly utility bill of more than $135

Explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

`\mu = 143, \sigma = 8`

What percentage of homes will have a monthly utility bill of more than $135?

We have to find 1 subtracted by the pvalue of Z when X = 135.

`Z = (X - \mu)/(\sigma)`

`Z = (135 - 143)/(8)`

`Z = -1`

`Z = -1` has a pvalue of 0.1587

1 - 0.1587 = 0.8413

84.13% of homes will have a monthly utility bill of more than $135