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Jack Jones is looking at buying a new cell phone plan and found one called "You Decide Your Minutes" Under this plan he would choose a quantity of minutes, say x, per month that she would buy at 5 cents per minute. Hence, his upfront cost would be $0.05x. If his usage is less than this quantity x in a given month, he loses the minutes. If his usage in a month exceeds this quantity x, he would have to pay 40 cents for each extra minute (that is, each minute used beyond x). For example, if he contracts for x=120 minutes per month and his actual usage is 40 minutes, his total bill is $120 x 0.05 = $6.00. However, if actual usage is 130 minutes his total bill would be $120 x 0.05 + (130 -120) x 0.40 = $10.00. Jack estimates that his monthly needs are best approximated by the Normal distribution with a mean of 250 minutes and a standard deviation of 24 minutes. How many minutes should he contract for?

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