The College Board National Office recently reported that in 20112012, the 547,038 high school juniors who took the ACT achieved a mean score of 515 with a standard deviation of 129 on the mathematics portion of the test (http://media.collegeboard.com/digitalServices/pdf/research/2013/TotalGroup-2013.pdf). Assume these test scores are normally distributed.

What is the probability that a high school junior who takes the test will score at least 590 on the mathematics portion of the test? If required, round your answer to four decimal places. P (x 590) =

What is the probability that a high school junior who takes the test will score no higher than 510 on the mathematics portion of the test? If required, round your answer to four decimal places. P (x 510) =

What is the probability that a high school junior who takes the test will score between 510 and 590 on the mathematics portion of the test? If required, round your answer to four decimal places. P (510 x 590) =

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? If required, round your answer to the nearest whole number.