SAT scores: Assume that in a given year the mean mathematics SAT score was 522, and the standard deviation was 116. Asample of 66 scores is chosen. Use the TI-84 Plus calculator.Part 1 of 5(a) What is the probability that the sample mean score is less than 509? Round the answer to at least four decimal places.The probability that the sample mean score is less than 509 isPart 2 of 5(b) What is the probability that the sample mean score is between 486 and 525? Round the answer to at least four decimalplaces.The probability that the sample mean score is between 486 and 525 isPart 3 of 5(c) Find the 90th percentile of the sample mean. Round the answer to at least two decimal places.The 90th percentile of the sample mean is