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# Exponential probability distribution for waiting times

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11.To harvest all the wheat from a field requires 5 sunny days (although not necessarily consecutive days) and a farmer only has one week left to get the job finished. Given that the probability of any day being sunny is 0.7, calculate the probability that the farmer will be able to get the wheat harvested in time.

12. Parents may help to save for their childrens university education using Registered Education Savings Plans (RESPs). Under the Canada Education Savings Grant Pro- gram, the government matches 20% of the parents contributions to an RESP (to an annual maximum). In addition, the income earned within an RESP is not taxed (the tax liability is deferred until the money is used for post-secondary education). In 2000, 7.2% of taxpayers with children under the age of 19 contributed to an RESP. An elementary school has 16 classrooms, each with 1 teacher and 20 students. During Parent-Teacher Interviews, each teacher asks the parents of the students in his or her class if they are contributing to an RESP for their son or daughter.

(a) What is the expected number of parents who contribute (for a given class).
(b) What is the probability that more than half of parents are contributing in a given class?
(c) What is the probability that 1/4 of the classes report more than 3 parents contributing?

13. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
(a) Find the probability of receiving three calls in a five-minute interval of time.
(b) Find the probability of receiving exactly 10 calls in 15 minutes?
(c) Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time?
What is the probability that none will be waiting?

14. Suppose the average waiting time to get food after placing an order at a fast-food restaurant is 60 seconds. Assume that an exponential probability distribution applies to the waiting times.
(a) What is the probability that a customer will wait 30 seconds or less?
(b) What is the probability that a customer will wait 45 seconds or less?
(c) What is the probability that a customer will wait more than 2 minutes