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# Statistics Problems

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J&G Painting has hired you as a consultant. You have been gathering data on its painting speed in an effort to help the company be more accurate in submitting bids. Based on data gathered after considering washing, taping, painting, and clean up, one person can paint an average of 100 square feet of indoor wall space per hour (because of extra taping time, doors and windows are counted as plain wall space), with a standard deviation of 12 square feet. The distribution of square feet painted is considered to be normally distributed.
A painter just started an 8-foot wide by 10-foot long room at 2:00 pm (assume an 8-foot high ceiling). The painter will be paid overtime if she is still working after 5:00pm. The ceiling is not to be painted.

a. How would you determine the probability overtime will not be paid?
b. How would you calculate the earliest the painter can expect to be finished with the room?
c. The painter is paid a "shop rate." This means that J&G Painting will charge a flat fee for the painting of the room. This charge is based on how long the particular job is expected to take. If the painter can finish the job earlier, she will receive half of the difference of the labor charged for how long the job was expected to take and how much time it actually took. The owner of the house was charged \$50 an hour and was told the job should take 3 hours. What is the largest amount of money the painter can make on this job over and above her salary?