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6. A company has a lump-sum incentive plan for its sales staff that is dependent on...

6. A company has a lump-sum incentive plan for its sales staff that is dependent on their level of sales. If they sell less than $100,000 per year they receive a $1000 bonus; from $100,000 to $200,000 they receive $5,000; and above $200,000 they receive $10,000. If the annual sales (per salesperson) follow a normal distribution with mu=$160,000 and sigma=$40,000:

a. Find the proportion of salespeople who receive a $1000 bonus.   (4 pts)

b. Find the proportion of salespeople who receive a $5000 bonus.   (4 pts)

c. Find the proportion of salespeople who receive a $10000 bonus.   (4 pts)

d. What is the mean value of the bonus payout for the company?   (6 pts)

7. You take your laundry to a laundromat and pay a quarter each time you run the dryer. After much study you have determined that the length of time the dryer runs on one quarter is a continuous uniform random variable bounded by 6 and 12 minutes. A pile of wet laundry needs 19 minutes of dryer time and you will use only one dryer. The amount of time that the dryer gives you for each quarter is independent.

a. Draw a picture of the probability density function for this situation and write the formula for this density function. (8 pts)

b. What is the average length of time the dryer will run on a quarter? (4 pts

c. What is the maximum probability that you will need more than three quarters to dry your pile of laundry? (8 pts)

Math   Statistics-And-Probability   
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