Reference no: EM13153725

1. At a carnival, the carousel ride has a problem with keeping the mechanical horses working. Repair technicians can be hired at a rate of $30 per hour, while working as only one team. This means the technician will work alone. If two or more techs are hired they work together on the same job. One technician can fix a horse in an average time of 20 minutes with standard deviation of 20 minutes. Two techs can fix a disabled horse in an average time of 15 minutes with standard deviation of 15 minutes. When a horse is down lost income is $50 per hour. Horses tend to break down at the rate of 2 per hour with the time between two consecutive breakdowns following an exponential distribution. 

If the carnival has the option of hiring one or two repairers, which option should the company choose?

2. 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?