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hardized variable Z = X - H will have the N(0,1) distribution. We will see how this standardization idea works through our next example. Try It! Scholastic Scores A proposal before the Board of Education has specified certain designations for elementary schools depending on how their students do on the Evaluation of Scholastic Scoring. This test is given to all students in all public schools in grades 2 through 4. Schools that score in the top 20% are labeled excellent. Schools in the bottom 25% are labeled "in danger" and schools in the bottom 5% are designated as failing. Previous data suggests that scores on this test are approximately normal with a mean of 75 and a standard deviation of 5. a. What is the probability that a randomly selected school will score below 70? b. What is the score cut-off required for schools to be labeled excellent? Show all work