Problem Set #5

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Problem Set #5 (Chapter 6) 3. Cincinnati to Tampa Flight Time. Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. a) Show the graph of the probability density function for flight time. b) What is the probability that the flight will be no more than 5 minutes late? c) What is the probability that the flight will be more than 10 minutes late? d) What is the expected flight time? 17. Height of Dutch Males. Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of males in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm. a) What is the probability that a Dutch male is shorter than 175 cm? b) What is the probability that a Dutch male is taller than 195 cm? c) What is the probability that a Dutch male is between 173 and 193 cm? d) Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm? 22. Television Viewing. Suppose that the mean daily viewing time of television is 8.35 hours. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household. a) What is the probability that a household views television between 5 and 10 hours a day? b) How many hours of television viewing must a household have in order to be in the top 3% of all television viewing households? c) What is the probability that a household views television more than 3 hours a day?
36. Comcast Service Interruptions. Comcast Corporation is a global telecommunications company headquartered in Philadelphia, PA. Generally known for reliable service, the company periodically experiences unexpected service interruptions. When service interruptions do occur, Comcast customers who call the office receive a message providing an estimate of when service will be restored. Suppose that for a particular outage, Comcast customers are told that service will be restored in 2 hours. Assume that two hours is the mean time to do the repair and that the repair time has an exponential probability distribution. a) What is the probability that the cable service will be repaired in 1 or less? b) What is the probability that the repair will take between 1 hour and 2 hours? c) For a customer who calls the Comcast office at 1: 00 p.m., what is the probability that the cable service will not be repaired by 5: 00 p.m.? 38. Boston 911 Calls. The Boston Fire Department receives 911 calls at a mean rate of 1.6 calls per hour (Mass.gov). Suppose the number of calls per hour follows a Poisson probability distribution. a) What is the mean time between 911 calls to the Boston Fire Department in minutes? b) Using the mean in part (a), show the probability density function for the time between 911 calls in minutes. c) What is the probability that there will be less than 1 hour between 911 calls? d) What is the probability that there will be 30 minutes or more between 911 calls? e) What is the probability that there will be more than 5 minutes, but less than 20 minutes between 911 calls?
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