STAT-UB103-The distribution of service times for a given task

Subject: Mathematics / Statistics
Question
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The distribution of service times for a given task is approximately normally distributed with mean 45 minutes and standard deviation 15 minutes.

1.Compute:

a.The percentage of tasks which are completed within one hour.

b.The 99th percentile of the distribution.

2.What is the probability that the service time is negative under the normal distribution assumption? Why is this probability greater than zero?

3.It costs $10 per hour in labor costs to complete the task. However, if a task is completed within 30 minutes, a bonus of $5 is awarded. What is the average labor cost associated with each task?

The annual rate of return on an equity fund is normally distributed with mean 12% and standard deviation 6%. The annual rate of return on an income fund is normally distributed with mean 10% and standard deviation 2%.

1.What is the probability that the rate of return on the equity fund will exceed 15%?

2.What is the probability that the equity fund will lose money (the annual rate of return will be less than 0)?

3.Find the 90th percentile of the equity fund’s rate of return.

4.The manager of the equity fund will receive an annual fixed salary of $70,000. He will receive a bonus of $50,000 if the fund will have a rate of return higher than 12%. The manager will receive an additional bonus of $100,000 if the fund will have a rate of return higher than 15%. What is his expected total salary?

NOTE: TOTAL SALARY = FIXED SALARY + BONUS

5.What is the probability that the rate of return on the income fund will be more than 8%?

6.What is the probability that the rate of return on the equity fund will be more than 8%?

7.Explain why the answer to (5) is greater than the answer to (6), even though the average rate of return of the income fund is less than the average rate of return on the equity fund.

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