3.46 Normal is only approximate: ACT scores. Composite scores on the ACT test for the 2015 high school graduating class had mean 21.0 and standard deviation 5.5. In all, 1,924,436 students in this class took the test. Of these, 205,584 had scores higher than 28, and another 60,551 had scores exactly 28. ACT scores are always whole numbers. The exactly Normal N(21.0, 5.5) distribution can include any value, not just whole numbers. What is more, there is no area exactly above 28 under the smooth Normal curve. So ACT scores can be only approximately Normal. To illustrate this fact, find

(a) the percent of 2015 ACT scores greater than 28 using the actual counts reported.

(b) the percent of 2015 ACT scores greater than or equal to 28, using the actual counts reported.

(c) the percent of observations that are greater than 28 using the N(21.0, 5.5) distribution. (The percent greater than or equal to 28 is the same, because there is no area exactly over 28.)