SAT scores: Assume that in a given year the mean mathematics SAT score was 467, and the standard deviation was 105. A sample of 59 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 455? Round the answer to at least four decimal places. The probability that the sample mean score is less than 455 is 0.8100 Going to work: A news report stated that the mean distance that commuters in the United States travel each way to work is 18 miles. Assume the standard deviation is 10 miles. A sample of 80 commuters is chosen. Part 1 of 2 (a) What is the probability that the sample mean commute distance is greater than 17 miles? Round the answer to at least four decimal places. The probability that the sample mean commute distance is greater than 17 miles is 0.8144 Part: 1/2 Part 2 of 2 (b) What is the probability that the sample mean commute distance is between 19 and 21 miles? Round the answer to at least four decimal places. The probability that the sample mean commute distance is between 19 and 21 miles is 5