NOTE: The numerical values in this problem have been modified for testing purposes. Suppose composite scores on the ACT test for the high school graduating class in a certain year had mean 20.9 and standard deviation 5.3. In all, 1,799,243 students in this class took the test. Of these, 170,777 had scores higher than 28 and another 54,167 had scores exactly 28. ACT scores are always whole numbers. The exactly Normal N(20.9,5.3) 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 ACT scores greater than 28 using the actual counts reported. (Enter your answer rounded to two decimal places.) percent: (b) the percent of ACT scores greater than or equal to 28, using the actual counts reported. (Enter your answer rounded to two decimal places.) percent: %

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NOTE: The numerical values in this problem have been modified for testing purposes.
Suppose composite scores on the ACT test for the high school graduating class in a certain year had mean 20.9 and
standard deviation 5.3. In all, 1,799,243 students in this class took the test. Of these, 170,777 had scores higher than 28
and another 54,167 had scores exactly 28. ACT scores are always whole numbers. The exactly Normal N(20.9, 5.3)
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 ACT scores greater than 28 using the actual counts reported. (Enter your answer rounded to two
decimal places.)
percent:
%
(b) the percent of ACT scores greater than or equal to 28, using the actual counts reported. (Enter your answer rounded
to two decimal places.)
percent:
%
Transcribed Image Text:NOTE: The numerical values in this problem have been modified for testing purposes. Suppose composite scores on the ACT test for the high school graduating class in a certain year had mean 20.9 and standard deviation 5.3. In all, 1,799,243 students in this class took the test. Of these, 170,777 had scores higher than 28 and another 54,167 had scores exactly 28. ACT scores are always whole numbers. The exactly Normal N(20.9, 5.3) 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 ACT scores greater than 28 using the actual counts reported. (Enter your answer rounded to two decimal places.) percent: % (b) the percent of ACT scores greater than or equal to 28, using the actual counts reported. (Enter your answer rounded to two decimal places.) percent: %
(c) the percent of observations that are greater than 28 using the N(20.9, 5.3) distribution. (The percent greater than or
equal to 28 is the same, because there is no area exactly over 28.) (Enter your answer rounded to two decimal places.)
percent:
%
Transcribed Image Text:(c) the percent of observations that are greater than 28 using the N(20.9, 5.3) distribution. (The percent greater than or equal to 28 is the same, because there is no area exactly over 28.) (Enter your answer rounded to two decimal places.) percent: %
Expert Solution
Step 1

Normal distribution:         

It is a continuous probability distribution, that is bell-shaped with lighter tails, symmetrical on both sides of the mean. The area under the normal distribution curve is the probability and the total probability is 1 similarly, the total area under the curve sums to 1.

In a normal distribution, the probability of a particular range is calculated by converting it into a standard normal and finding the value in the Standard normal distribution table.

Z=x-μσ

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