Here are some sample test questions for Chapter 2. These questions also review some aspects of chapters 7 and 8. The test for Chapter 2 also may touch on those topics. Always interpret the problem and explain your solution.

1. A student takes a county-wide math test and scores an 82. She wants to know her pcercentile, but all that the county will say is that 50 percent of all students scored between 66 and 76. Assuming that the distribution of scores is normal, what would you tell her is her percentile?

2. Suppose that the probability distribution of your grade on any statistics quiz is normally distributed with a mean of 80 and a standard deviation of 12. If you take 15 quizzes in a year, what is the expected number of times that you get below 60? What is the expected number of quizzes that you take before you get below 60?

3. You go to hear a lecture on health, and the speaker says that:

   • People who smoke but are not obese are in the 75th percentile for heart disease
   • People who are obese but do not smoke are in the 70th percentile for heart disease
   • The overall mean incidence of heart disease is 5 percent
   • People who are obese but do not smoke have an incidence of heart disease of 9 percent.

   What is the incidence of heart disease in people who smoke but are not obese?

4. Suppose that in math your mean test score is 80 with a standard deviation of 15 percent, and in English your mean test score is 75 with a standard deviation of 10 percent. If you get below 60 percent you fail.
   • Are you more likely to fail a math test or an English test?
   • Assume that the test results are independent. If you could combine an English test and a math test and take the average score, what would be the mean and the standard deviation? What would be the probability of failure?