Problem
Assume that in a given year the mean mathematics SAT score was 572, and the standard deviation was 127.A sample of 72scores is chosen.
1. What is the probability that the sample mean score is less than 567? Round the answer to at least four decimal places.
2. What is the probability that the sample mean score is between 537and 580? Round the answer to at least four decimal places.
3. Find the 60th percentile of the sample mean. Round the answer to at least two decimal places.
4. Would it be unusual if the sample mean were greater than 580? Round the answer to at least four decimal places.
5. Do you think it would be unusual for an individual to get a score greater than 580? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.