The College Board National Office recently reported that in 2011-2012, the 547,038 high school juniors who took the ACT achieved a mean score of 530 with a standard deviation of 123 on the mathematics portion of the test (media.collegeboard.com/digitalServices/pdf/research/2013/TotalGroup-2013.pdf). Assume these test scores are normally distributed.
a. What is the probability that a high school junior who takes the test will score at least 610 on the mathematics portion of the test?
b. What is the probability that a high school junior who takes the test will score no higher than 460 on the mathematics portion of the test?
c. What is the probability that a high school junior who takes the test will score between 460 and 550 on the mathematics portion of the test?
d. How high does a student have to score to be in the top 10% of high school juniors on the mathematics portion of the test?