Normal Probability Distribution

Instructions: Read the scenario and answer the questions below. Round all probabilities and proportions to 4 decimal places.

The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students' scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation 8.8. (Source:www.ets.org). A graduate school requires that students score above 160 to be admitted.

1. What proportion of combined GRE scores can be expected to be over 160?
2. What proportion of combined GRE scores can be expected to be under 160?
3. What proportion of combined GRE scores can be expected to be between 155 and 160?
4. What is the probability that a randomly selected student will score over 145 points?
5. What is the probability that a randomly selected student will score less than 150 points?
6. What is the percentile rank of a student who earns a quantitative GRE score of 142?
7. Historically, Depart of History at NYU has admitted students whose quantitative GRE score is at least at the 61^st percentile. (Source: history.fas.nyu.edu/object/admissions.faq.html.) What is the lowest GRE score of the students they admit?
8. Determine the 80^th percentile of combined GRE scores.
9. Determine the combined GRE scores that make up the middle 95% of all scores?

Use the standard normal distribution to determine the following:

68% of the scores lie between what two values?

95% of the scores lie between what two values?

99% of the scores lie between what two values?