Marisol is new to town and is in the market for cellular phone service. She hassettled on Wildcat Cellular, which will give her a free phone if she signs a one-yearcontract. Wildcat offers several calling plans. One plan that she is considering iscalled “Pick Your Minutes”. Under this plan, she would specify a quantity of minutes,say x, per month that she would buy at 15¢ per minute. Hence, her upfront costwould be $0.15x. If her usage is less than this quantity x in a given month, she losesthe minutes. If her usage in a month exceeds this quantity x, she would have to pay40¢ for each extra minute (that is, each minute used beyond x). For example, if shecontracts for x=120 minutes per month and her actual usage is 40 minutes, her totalbill is $120 × 0.15 = $18.00. However, if actual usage is 130 minutes, her total billwould be $120 × 0.15 + (130 – 120) × 0.40 = $22.00. The same rates apply whetherthe call is local or long distance. Once she signs the contract, she cannot change thenumber of minutes specified for a year
Marisol estimates that her monthly needs are best approximated by the Normaldistribution, with a mean of 250 minutes and a standard deviation of 24 minutes
a) What is the probability that Marisol uses more than 270 minutes?
b) If Marisol chooses the “Pick Your Minutes” plan described above, how manyminutes should she contract for?
c) Marisol really dislikes prepaying too many minutes and not usingthem. How many minutes should she purchase so that the probabilityshe does not use them all is no more than 10%?