Reference no: EM132855945

1. Approximately what percentage of cases is within ± 1 standard deviation of the mean for a normally distributed variable?

2. Imagine that you ask people their opinions about a new policy, and you find that their opinions are approximately normally distributed. Below are four descriptions of this result. Arrange them in order from most accurate and complete to least accurate and complete.

a) Most people hold opinions that are fairly similar, though a few individuals endorse opinions that are very different from the majority.

b) Opinions are sharply divided, with two groups of individuals holding very different opinions.

c) There is very little that we can say, except that people hold a wide range of opinions.

d) Most people endorse opinions that are similar, though a few individuals hold opinions that are much weaker or stronger than the majority.

SAT scores are normed so that in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. Assuming this is true (it is only approximately true, both because of variation from year to year and because scores have decreased since the SAT tests were first developed), answer questions 3 - 5.

3. What percentage of students score above 625 on the math SAT in any given year?

4. What percentage of students score between 400 and 600 on the verbal SAT?

5. A college decides to liberalize its admission policy. As a first step, the admissions committee decides to exclude only those applicants scoring below the 20th percentile on the verbal SAT. Translate this percentile into a Z score. Then calculate the equivalent SAT verbal test score.