Part 1 Scores for a common standardized college aptitude test are normally distributed with a mean of 497 and a standard deviation of 115. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect.
If 1 of the men is randomly selected, find the probability that his score is at least 599.9.
P(X > 599.9) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
If 5 of the men are randomly selected, find the probability that their mean score is at least 599.9.
P(M > 599.9) =
Part 2
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 197.4-cm and a standard deviation of 1.6-cm. For shipment, 13 steel rods are bundled together.
Find the probability that the average length of a randomly selected bundle of steel rods is greater than 198.5-cm.
P(M > 198.5-cm) =