Statistics 112
Normal Distribution and Sampling Distribution Problems
1. The scores on the GRE Mathematics test follow a normal distribution with mean 500 and
standard deviation 100. Graduate Division has suggested that applicants in the mathematical
sciences (math, statistics, physics, engineering etc.) should have a GRE math score of 700
or above. What percentage of the GRE examinees should an applicant to a Math graduate
program score better than? In other words, in what percentile should the applicant score?
2. The pH of randomly selected follows a normal distribution with mean 7.4 and standard
deviation 0.22. A pool should have a pH between 7.2 and 7.8 so that chlorine treatment is
effective. What percentage of pools have an acceptable pH level?
3. On a standardized test with mean 50 and standard deviation 20, what is the probability that
a student scores a 100?
4. At a typical pond taken over by Mallard ducks, the average weight of a duck in the pond
is 2 pounds. A biologist is concerned that there is something wrong with the pond. The
average weight of a Mallard duck is 2.6 pounds with a standard deviation of 0.4 pounds.
What percentage of these special ponds have an average duck weight greater than this pond?
Assume that exactly 50 ducks were weighed at each pond.
1
