Assume that the distribution of scores in a Statistics test is normal, with = 100 and = 15.

1. What is the probability that a score is 120? (Hint: Find thez-scores of the real limits and the difference between the probabilities.) (4 pts)
2. What is the probability that a score is below 90? (4 pts)
3. What is the probability that a score is between 130 and 85? (Hint: Find the z-score of each, then combine the probabilities.) (4 pts)
4. What is the percentile rank of X = 105? (Hint: The answer is based on thez-score of X = 105.) (4 pts)
5. What proportion of the scores is above the 80th percentile? (Hint: This is a conceptual question to determine your understanding of percentile; no solutions required.) (4 pts)