OPS MGMT – Jack Jones is looking at buying a new cell phone plan

Jack Jones is looking at buying a new cell phone plan and found one called “You DecideYour Minutes” Under this plan he would choose a quantity of minutes, say x, per month thatshe would buy at 5 cents per minute. Hence, his upfront cost would be $0.05x. If his usageis less than this quantity x in a given month, he loses the minutes. If his usage in a monthexceeds this quantity x, he would have to pay 40 cents for each extra minute (that is, eachminute used beyond x). For example, if he contracts for x=120 minutes per month and hisactual usage is 40 minutes, his total bill is $120 x 0.05 = $6.00. However, if actual usage is130 minutes his total bill would be $120 x 0.05 + (130 -120) x 0.40 = $10.00. Jack estimatesthat his monthly needs are best approximated by the Normal distribution with a mean of 250minutes and a standard deviation of 24 minutes. How many minutes should he contract for?