Suppose that the distribution of weekly water usage for single-family homes in a particular city is approximately normal. The mean is 1400 gallons, and the standard deviation is 300 gallons.

Question

a. What is the z-score for 800 gallons?

b. What is the approximate value of the highest 15th percentile?

c. What is the 7-score for 1665 gallons?

d. What is the approximate value of the 14th percentile?

e. What is the percentile for 749 gallons? f. What is the approximate value of the 50th percentile?

Answer 1

Either you use a table or technology to solve this problem. If you use technology, you need to use the right method given that technology and the answer is provided.

1) z = (x-mu)/sigma you are given x = 800 and mean (mu) and standard deviation (sigma)

2) You need to solve for x given that you look for the z value in a table that gives you .85 probability that the x is to the left (If you have a right tail table, you need to use .15). Once you have the z, you can use the definition of z in (1) to solve for x = sigma*z + mu.

3) same as (1), different x

4) Same as (2), but you want left of .14 or right of .86

5) Same as (1), then use the z to find the percentile (left tail).

The second part is just x = mu

Please consider a tutor.