# statistics

posted by .

The average electric bill in a residential area is \$72 for the month of May. The standard deviation is \$6. If the amounts of electric bills are normally distributed, find the probability that the mean of the bill for 15 residents will be less thatn \$75

• statistics -

You need to work out the standard deviation of the mean of the bill for 15 residents. That's \$6//sqrt(15), which is 1.549. So the distribution of the mean of the bill for 15 residents will be Normal, with mean \$72 and standard deviation 1.549. You have to work out the probability that the mean will be less than \$75, so you need work out how many standard deviations \$75 is above \$72, which is (\$75 - \$72) divided by \$1.549, which is 1.936. You now need to know what the area to the left of that point (because you want the probability of the mean bill being less that \$75) is, and you can get that from a set of Normal probability tables. If you were looking up 1.96 you would get an answer of 0.975, so you know it's going to be a bit less than that. I've just looked it up myself, and I get 0.9735 - so I reckon that's your answer - i.e. just over 97%.

## Similar Questions

1. ### Math Quantitive Reasoning

The amount of Jen's monthly phone bill is normally distributed with a mean of \$50 and a standard deviation of \$12. What percentage of her phone bills are between \$14 and \$86?
2. ### Math

Use the 68-95-99.7 rule to solve the problem. - The amount of Jen's monthly phone bill is normally distributed with a mean of \$53 and a standard deviation of \$11. What percentage of her phone bills are between \$20 and \$86?
3. ### Statistics

The amount of a monthly phone bill is normally distributed with a mean of \$60 and a standard deviation of \$12. Fill in the blanks: 68% of her phone bills are between \$______________ and \$______________.
4. ### Statistics

Electricity bills in a certain city have mean \$120.08. Assume the bills are normally distributed with standard deviation \$14.40. Find the value that separates the lower 52% of the bills from the rest.
5. ### statistics

The customer bills in a family restaurant are normally distributed. The bills mean is \$28 and has a standard deviation of \$6. a. Identify what the random variable you are measuring is in this problem. b. What is the probability that …
6. ### statistics

The diameter of an electric cable is normally distributed, with a mean of 0.6 inch and a standard deviation of 0.02 inch. What is the probability that the diameter will exceed 0.62 inch?
7. ### Math

The amount of Jen's monthly phone bill is normally distributed with a mean of \$55 and a standard deviation of \$9. Within what range are 68% of her phone bills?
8. ### algebra

The amount of Jen's monthly phone bill is normally distributed with a mean of \$55 and a standard deviation of \$9. Within what range are 68% of her phone bills?
9. ### math

the amount of jens month phone bill is normally distributed with a mean of \$69 and a standard deviation of \$10. what is 68.26% of phone bill between?
10. ### Statistics

The amount of Jen's monthly phone bill is normally distributed with a mean of \$55 and a standard deviation of \$12. Calculate the z score for each scenario. What percentage of her phone bills are above 79?

More Similar Questions