A research polls a sample of cold sufferers and askes them to estimate the number of hours of physical discomfort caused by their cold. Their estimates approximate a normal curve with a mean of 83 hours and a standard deviation of 20 hours.

1. What is the estimated number of hours for the shortest-suffering 5 percent?
2. What proportion of sufferers estimated that their colds lasted longer than 2 days?
3. What propostion suffered for fewer than 61 hours?
4. What is the estimate number of hours for the extreme 1 percent in either direction from the mean?
5. What proportion suffered for between one and three days?
6. What is the estimated number of hours for the shortest-suffering 10 percent?
7. What is the estimated number of hours for the middle-suffering 95 percent?
8. What proportion suffered for between two and four days?

1. If applicants with GPAs of 3.50 or above are automatically admitted, what proportion of applicants will be in this category?
2. If applicants with GPAs of 2.50 or below are automatically denied admission, what proportion of applicants will be in this category?
3. A special honors program is open to all applicants with GPAs of 3.75 or better. What proportion of applicants are eligible?
4. If the special honors program is limited to students whose GPAs rank in the upper 10 percent, what GPA will be required for admission to this program?

Try using the zscore calculator at http://www.duxbury.com/authors/mcclellandg/tiein/howell/zcalc.htm
 
 Z score problems on the web

Click here   for  James M. Hillenbrand's (Western Michigan University) problems.

Another helpful z-score quiz is here.

Here is a set of problems from Memorial University and here are the answers.

Several of these problems make reference to percentiles.  If you are unfamiliar with the term, here's a definition:
Percentiles rank the position of an individual by indicating what percent of the reference population the individual would equal or exceed. For example, on the weight-for-age growth charts, a 5-year-old girl whose weight is at the 25th percentile, weighs the same or more than 25 percent of the reference population of 5-year-old girls, and weighs less than 75 percent of the 5-year-old girls in the reference population.