What is the probability that exactly seven of the students plan to pursue a graduate degree?

Statistics
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Q1. In the University of Michigan-Dearborn, about 35% of recent college graduates plan to pursue a graduate degree. Now if we randomly select fifteen recently graduated UMD students and ask them whether they want to pursue a graduate degree. 1. What is the probability that exactly seven of the students plan to pursue a graduate degree? 2. What is the probability that no more than five of the students plan to pursue a graduate degree? 3. What is the probability that at least six but no more than nine of the students plan to pursue a graduate degree? UMID: ________________________ Name: _________________________ Q2. DTE has a customer service center near Dearborn to handle customers encountering power outage. The average call is about 350 calls a day. Suppose the service center is staffed for 16 hours a day. 1. Calculate the average number of calls in a one-hour interval, 30-minutes interval, and 15-minutes interval. 2. What is the probability of exactly six calls in a 15-minutes interval? 3. What is the probability of no calls in a 15 minutes intervals? 4. What is the probability of at least two calls in a 15 minutes interval? Q3. You have a bag with ten skittles, of which five are green and five are yellow. If you draw two to eat, what is the probability that both skittles are yellow? What is the probability that at least one of them is green?

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