Question

Electricity bills: According to a government energy agency, the mean monthly household electricity bill in the United States in 2011 was $109.72. Assume the amounts are normally distributed with standard deviation $24.00. Use the TI-84 Plus calculator to answer the following. (a) What proportion of bills are greater than $131

Answer 1

18.67% of bills are greater than $131

Explanation:

Problems of normally distributed samples are solved using 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 problem, we have that:

`\mu = 109.72, \sigma = 24`

What proportion of bills are greater than $131

This proportion is 1 subtracted by the pvalue of Z when X = 131. So

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

`Z = (131 - 109.72)/(24)`

`Z = 0.89`

`Z = 0.89` has a pvalue of 0.8133

1 - 0.8133 = 0.1867

18.67% of bills are greater than $131