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Mario14b_Spring08 - MATH 218 SI Session(Spring 2008 SI...

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MATH 218 SI Session (Spring 2008) SI Leader: Mario Week 14 Worksheet Tuesday (4/15/08) Professor: Zygouras/Dumett www.usc.edu/si 1. The number of students entering the bookstore is Poisson distributed with an average rate of 2 students every 3 minutes. a. What is the probability that at most 1 student enters the bookstore in the next 2 minutes? b. Find the probability that the next student arrives within half a minute. c. What is the probability that no students enter within the next two minutes? d. What is the average time between students? 2. With the high demand for many of the new video consoles, there is only a 25% chance that any store will carry the exact system that you are looking for this holiday season. a. Suppose we decided to visit 20 different stores. What is the probability that we find the system that we want at exactly 5 out of the 20 stores? b. Find the expected value and standard deviation for the number of stores that carry the system that you are looking for. c. What is the probability that more than 18 out of the 20 stores carry the system that we are looking for?
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3. The Elgin Heart Institute performs many open-heart surgery procedures. Recently research physicians at Elgin have developed a new heart bypass surgery procedure that they believe will reduce the average recovery time. The hospital will not recommend the new procedure unless there is substantial evidence to suggest that it is better than the existing procedure. Records indicate that the current mean recovery time for the standard procedure is 42 days, with a standard deviation of 5 days. To test whether the new procedure actually results in a lower mean recovery time, it was performed on a random sample of 36 patients. Assume the standard deviation remains 5 days.
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