According to the U.S. Energy Information Administration, the mean monthly househ

Question

According to the U.S. Energy Information Administration, the mean monthly household electric bill in the U.S. in 2007 was $99.70 with a standard deviation of $20. Assume the amounts are normally distributed. In the winter bills can run higher than usual due to colder temperatures. To help customers cope with the higher costs in winter, an electric supplier offers a payment plan for customers with costs in the top 4% of all electric bills. What bill amount would a customer have to exceed to be offered the payment plan? Give your answer to 2 decimal places. (Do NOT include the $ sign)

Explanation / Answer

From information given, mu=99.70, sigma=20. It is also known that z score corresponding to top 4% of all electric bills is: 1.75 (look into standard normal table to find z score corresponding to 0.04).

Now, substitute the values in following z score formula to find the raw score, which corresponds to the amount a customer has to exceed to be offered the payment.

z=(x-mu)/sigma, where, x is the raw score.

1.75=(x-99.70)/20

x=134.7 (ans)

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