Applied Statistics HW 6

1. In a test, students receive a grade from 1 to 100. In a class consisting of about 500 students, their test scores follow an approximately normal distribution, with a mean of 76.5 and a standard deviation of 10.3.
   1. Students who scored 95 and above would get an A. Approximately how many students would that be?
   2. How many students approximately scored in the B range of 80 to 90?
   3. What was the first quartile score?
   4. The teacher will assign an F to those students that scored 60 or below. How many students approximately would that be?
2. Batting averages for baseball players are approximately distributed, and have an average of 0.278 with a standard deviation of 0.02.
   1. We could call someone an exceptional batter, if his batting average is in the top 1% of all batting averages (BA). What BA does such a batter need to have, at least?
   2. Provide a range of batting averages that would encompass 99.9% of all BAs.
   3. A certain batter scored a 0.267. What percentile is that value?