1) Reports on a student's ACT or SAT usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were...

1) Reports on a student's ACT or SAT usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one. In 2007, composite ACT scores were close to Normal with mean 21.2 and standard deviation 5.0. Jacob scored 16. What was his percentile?

2) It is possible to score higher than 1600 on the SAT, but scores 1600 and above are reported as 1600. In 2007 the distribution of SAT scores (combining mathematics and reading) was close to Normal with mean 1021 and standard deviation 211. What proportion of 2007 SAT scores were reported as 1600?

3) The heights of women ages 20 to 29 follow approximately the N(64, 2.7) distribution. Men the same age have heights distributed as N(69.3, 2.8). What percent of young women are taller than the mean height of young men?

4) The heights of women ages 20 to 29 follow approximately the N(64, 2.7) distribution. Men the same age have heights distributed as N(69.3, 2.8). What percent of young men are shorter than the mean height of young women?