The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of9.9minutes and a standard deviation of2.9minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes (b) longer than 5 minutes (c) between 8 and 15 minutes

Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency, duration, and type of use. One study involving heavy use of the phones showed the mean of the battery life to be10.75hourswith a standard deviation of3.3hours.Then the battery needs to be recharged. Assume the battery life between charges is normally distributed.

(a) Find the probability that with heavy use, the battery life exceeds11hours. (Round your answer to four decimal places.) (b) You are planning your recharging schedule so that the probability your phone will die is no more than 5%. After how many hours should you plan to recharge your phone? (Round your answer to the nearest tenth of an hour.) hours

Express Courier Service has found that the delivery time for packages is normally distributed, with mean13hours and standard deviation2hours.

(a) For a package selected at random, what is the probability that it will be delivered in 18 hours or less? (Round your answer to four decimal places.) (b) What should be the guaranteed delivery time on all packages in order to be95%sure that the package will be delivered before this time? (Hint:Note that5%of the packages will be delivered at a time beyond the guaranteed time period.) (Round your answer to one decimal place.) hr

24.

The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean=$627and standard deviation=$47.

(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.) (b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only0.14? (Round your answer to the nearest dollar.) $