1. Scores for a common standardized college aptitude test are normally distributed with a mean of 508 and a standard deviation of 101. 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 572. P(X > 572) = Round to 4 decimal places. If 11 of the men are randomly selected, find the probability that their mean score is at least 572. P(XX > 572) = Round to 4 decimal places. If the random sample of 11 men does result in a mean score of 572, is there strong evidence to support the claim that the course is actually effective?

• Yes. The probability indicates that it is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 572.
• No. The probability indicates that it is possible by chance alone to randomly select a group of students with a mean as high as 572.

2. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 163-cm and a standard deviation of 1.2-cm. For shipment, 8 steel rods are bundled together.

Find P₈₅, which is the average length separating the smallest 85% bundles from the largest 15% bundles.

P₈₅ = cm Round to 2 decimal places.

3.Suppose 11% of students are veterans and 148 students are involved in sports. How unusual would it be to have no more than 7 veterans involved in sports? (7 veterans is about 4.7297%) When working with samples of size 148, what is the mean of the sampling distribution for the proportion of veterans? When working with samples of size 148, what is the standard error of the sampling distribution for the proportion of veterans? Compute P(pp^ 0.047297). P(pp^ 0.047297) = NOTE: Give results accurate to 5 decimal places

4. Suppose 7% of students are veterans and 130 students are involved in sports. How unusual would it be to have no more than 7 veterans involved in sports? (7 veterans is about 5.3846%) When working with samples of size 130, what is the mean of the sampling distribution for the proportion of veterans? When working with samples of size 130, what is the standard error of the sampling distribution for the proportion of veterans? Compute P(pp^ 0.053846). P(pp^ 0.053846) = NOTE: Give results accurate to 5 decimal places

5. The lengths of pregnancies in a small rural village are normally distributed with a mean of 265 days and a standard deviation of 15 days. In what range would you expect to find the middle 98% of most pregnancies? Between and . If you were to draw samples of size 42 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample? Between and . Enter your answers as numbers. Your answers should be accurate to 1 decimal places.