Suppose the amount of tar in cigarettes is described by a normal model with a mean of 3. 5 mg and a standard deviation of 0. 5 mg. a. What proportion of cigarettes have a tar content that exceeds 4. 25 mg? b. In order to advertise as a low tar brand, a manufacturer must prove that their tar content is below the 25th percentile of the tar content distribution. Find the 25th percentile of the distribution of tar amounts. 11. Has the percentage of young girls drinking milk changed over time? The following table is consistent with the results from “Beverage Choices of Young Females: Changes and Impact on Nutrient Intakes” (Shanthy A.
Bowman, Journal of the American Dietetic Association, 102(9), pp. 1234-1239): Nationwide Food Survey Years 1987-1988 1989-1991 1994-1996 354 502 366 226 335 366 580 837 732 Drinks Fluid Milk a. 1. 2. 3. 4. Total Yes 1222 No 927 Total 2149 Find the following: What percent of the young girls reported that they drink milk? What percent of the young girls were in the 1989-1991 survey? What percent of the young girls who reported that they drink milk were in the 1989-1991 survey? What percent of the young girls in 1989-1991 reported that they drink milk? b. What is the marginal distribution of milk consumption? 12.
It’s the last inning of an important baseball game. The home team is losing by a run, the bases are loaded and the manager needs a pinch hitter. Two batters are available to pinch hit. Here are their statistics: Player Overall vs Left-handed pitching vs Right-handed pitching A 33 for 103 28 for 81 5 for 22 B 45 for 151 12 for 32 33 for 119 Based on their overall batting averages and their batting averages against right-handed and left-handed pitchers, who would you select as the pinch hitter? What is this phenomenon called? 13. The mean SAT verbal score of next year’s freshmen entering the local university is 600.
It is also known that 69. 5% of these freshmen have scores that are less than 625. If the scores can be described by a normal model, what is the standard deviation of the scores? 14. Two students are enrolled in an introductory statistics course at the University of Florida. The first student is in a morning section and the second student is in an afternoon section. If the student in the morning section takes a midterm and earns a score of 76, while the student in the afternoon section takes a midterm with a score of 72, which student has performed better compared to the rest of the students in his respective class?