We can use the z-score to find the probability of many other events. Let's explore those now.

a. Suppose that the mean time a typical American teenager spends doing homework each week is 4.2 hours. Assume the standard deviation is 0.9 hour. Assuming the variable is normally distributed, find the percentage of American teenagers who spend less than 3.5 hours doing homework each week.

b. According to a College Board report, the population of American 2008 high school graduates had a mean Math SAT score of 515 with standard deviation of 116. What is the probability that of a randomly selected senior from this population scoring between 500 and 800 on the Math portion of the SAT Reasoning Test?