This homework has 4 questions to hand-in. Write down all details of your solutions, not just the answers. Show your reasoning. Please staple the pages together and clearly PRINT your name on the first page of the problem set. Cooperation on problems is permitted, but all solutions must be written up independently and you must list your collaborators on the problem set. You should first try to solve each problem yourself, otherwise you will not learn much from hearing the solution. Also, all the questions listed below are similar to the practice problems you attempted under Test Your Understanding.
1. The number of adults living in homes on a randomly selected city block is described by the following probability distribution. What is the standard deviation of the probability distribution?
|Number of adults, x||1||2||3||4||5|
2. Molly earned a score of 950 on a national achievement test. The mean test score was 850 with a standard deviation of 100. What proportion of students had a higher score than Molly? (Assume that test scores are normally distributed.)
3. Suppose scores on an IQ test are normally distributed. If the test has a mean of 90 and a standard deviation of 10, what is the probability that a person who takes the test will score between 80 and 100?
4. Assume that a school district has 20,000 5th graders. In this district, the average weight of a 5th grader is 80 pounds, with a standard deviation of 20 pounds. Suppose you draw a random sample of 100 students. What is the probability that the average weight of a sampled student will be less than 70 pounds?
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