THE NORMAL DISTRIBUTION

Name___________________________

(Printed)

Student Number___________________

(Social Security Number)

E-mail__________________________

These questions are based on Agresti and Finlay, Statistical Methods, chapter 4.

1. In 1992 the murder rate (per 100,000 residents) for 74 major U.S. cities had a mean of 20.8 and a standard deviation of 14.6 (Statistical Abstract of the United States, 1994).
1. One of these cities, Washington, D.C., had a murder rate of 75.2. Find its z-score:__________________
2. If the distribution were roughly normally distributed, would this be an unusually high value? Why?

______________________________________________________________________________________________________________________________________________________________________________________________________

1. What is the murder rate of a city that has a z-score of 0.0? (You should be able to figure this out without doing any calculations.)______________



1. Suppose the property taxes on homes in Gainesville, Florida are approximately normal in distribution, with a mean of $1,400 and a standard deviation of $600. The property tax for one particular home is $1,700.
1. Find the z-score corresponding to that value._________________
2. What proportion of the property taxes exceed $1,700?_____________
3. Now, in fact the distribution of property taxes is "mound-shaped" (i.e., has a single peak or hump) but is not normal. What would you expect it to look like?

1. Suppose that the weekly use of gasoline for motor travel by adults in the United States is approximately normally distributed with a mean of 16 gallons and a standard deviation of 5 gallons.
1. What proportion (or percent) of adults use 20 or more gallons a week?

• Any questions? H. T. Reynolds

Go to Statistics 815 main page

Go to H. T. Reynolds page.