Scores on the ACT test for the 2010 high school graduating class had mean 21.0 and standard deviation 5.2. In all, 1,568,835 students in this class took the test. Of these, 145,000 had scores higher than 28 and another 50,860 had scores exactly 28. ACT scores are always whole numbers. The exactly Normal N(21.0, 5.2) 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 2010 ACT scores greater than 28. (b) the percent of 2010 ACT scores greater than or equal to 28. (c) the percent of observations from the N(21.0, 5.2) distribution that are greater than 28. (The percent greater than or equal to 28 is the same, because there is no area exactly above 28.)
Scores on the ACT test for the 2010 high school graduating
class had mean 21.0 and standard deviation 5.2. In all,
1,568,835 students in this class took the test. Of these,
145,000 had scores higher than 28 and another 50,860 had
scores exactly 28. ACT scores are always whole numbers.
The exactly Normal N(21.0, 5.2) 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 2010 ACT scores greater than 28.
(b) the percent of 2010 ACT scores greater than or equal
to 28.
(c) the percent of observations from the N(21.0, 5.2) distribution that are greater than 28. (The percent greater than or equal
to 28 is the same, because there is no area exactly above 28.)
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