my math homework and I need help

Question

Suppose that water usages in American showers are normally distributed, with an average shower using 16.8 gallons, and a standard deviation of 2.5 gallons. Estimate the percentage of showers that used

(a) between 11.8 and 21.8 gallons.

 %

(b) more than 24.3 gallons.

 %

(c) less than 14.3 gallons.

 %

(d) between 9.3 and 21.8 gallons.

 %

Answer 1

Need to calculate the z factor for each of the scenarios and use a table to determine the probabilities that the values will be less that the value given. The normal distribution tables show the area under the normal distribution curve (probability) to the left of the value ("less than"). For "more than" use 1 - the z-score. For "between" calculate the probabilities for each end of the spread and subtract.

z = (x - µ)/σ, where x is the value of water used, μ is the mean (16.8), and σ is the std. deviation (2.5).

Answer 2

List the mean and the standard deviations

8.5 11.8 14.3 16.8 19.3 21.8 25