1. A teacher gives the following assignment to 200 students: Check the local newspaper every morning for a week and count how many times the word "gun" is mentioned on the "local news" pages. At the end of the week, the students report their totals. The mean result is 85, with a standard deviation of 8. The distribution of scores is normal.

a. How many students would be expected to count fewer than 70 cases?

b. How many students would be expected to count between 80 and 90 cases?

c. Karen is a notoriously lazy student. She reports a total of 110 cases at the end of the week. The professor tells her that he is convinced she has not done the assignment but has simply made up the number. Are his suspicions justified?

2. A noted criminologist, Leslie Wilkins, has suggested that the distribution of deviance in the population follows a normal bell-shaped curve, with "sinners" at one extreme, "saints" at the other, and most of us falling somewhere in between the two. Working on the basis of this theory, a researcher constructs a detailed self-report survey whereby individuals are given a score based on the offenses they have committed in the past year, with the score weighted according to the relative triviality or seriousness of each offense. The lower the score, the nearer the individual approximates "sinner" status, and the higher the score, the closer he or she is to being a "saint." From his initial sample of 100 adults in a specific state, the researcher computes a mean score of 30, with a standard deviation of 5. a. If the researcher's model is correct, below which score should he expect to find the 5% of U.S. society with the greatest propensity to deviance? b. In his sample of 100, the researcher is surprised to discover that 50 subjects score greater than 35 on the deviance test. How many cases would be expected under the assumption of a normal distribution of saints and sinners? What does this suggest about the original theory?