Question

Suppose that composite scores on the ACT test for the school graduating class in a certain year had a mean of 24.2 and a standard deviation of 4.6. In all, 1,823,241 students in this class took the test, and of these, 6,947 had scores higher than 36.4 and 2,404 had scores exactly 36.4. ACT scores are always whole numbers, but the Normal N(24.2, 4.6) distribution can include any value, not just whole numbers. What is more, there is no area exactly above 36.4 under the smooth Normal curve, so ACT scores can only be approximately Normal. To illustrate this fact find: The proportion of ACT scores greater than 36.4 using the N(24.2, 4.6) distribution, which is the same as the percent of ACT scores greater than or equal to 36.4 using the N(24.2, 4.6) distribution. (Round your z-score to two decimal places and enter your answer as a proportion rounded to four decimal places)

Answer 1

Given that population mean is 24.2 and standard deviation is 4.6.

Finding P(X>36.4)