This problem is in reference to students who may or may not take advantage of the opportunities provided in QMB such as homework. Some of the students pass the course, and some of them do not pass. Research indicates that 40% of the students do the assigned homework. Of the students who do homework, there is an 80% chance they will pass the course. The probability of not passing if the student does not do the home work is 90%. What is the probability of a student not doing homework or passing?
A. .32
B. .52
C. .94
D. .92
E. .38
2. Suppose that for a certain football game the probability that the home team will be ahead at half-time is 0.60 and the probability that the home team will be ahead at half- time as well as at the final gun is 0.45. What is the probability that the home team will win this game given that it is ahead at the half?
A. .45
B. .75
C. .15
D. .27
E. None of the above.
3. A company markets two products (Product A and Product B) through mail order. The company will market them in sequence with the first mail order offer for product A. It f feels that there is a 30% chance that any customer will purchase product A. Product B is offered some months later. It is felt, for product B, that there is a 30% chance of selling product B to a customer if the customer purchased product A and a 5% chance of selling product B to a customer who did not purchase product A.
What is the probability of not selling product B to a particular customer?
A. .875
B. .665
C. .125
D. .210
E. None of the above
4. A quality control department finds that it accepted only 5% of all bad items and it rejected only 1% of good items. A supplier has just delivered a shipment of a certain item. Past records show that only 90% of the parts of that supplier are good. If the department accepts an item, what is the probability that the item is bad? Round your answer to five decimal places.
A. 0.05000
B. 0.00558
C. 0.35714
D. 0.09635
E. None of the above
5. The probability that house sales will increase over the next six months is estimated at 0.25. It is also estimated that the probability is 0.74 that 30 year fixed-loan mortgage rates will increase over this period. Economists estimate that the probability is 0.89 that either housing sales or interest rates will increase.
The probability that both house sales and interest rates will increase is estimated at:
A. .100
B. .185
C. .705
D. .900
E. .500
6. Over the last 100 business days, Harry had 20 customers on 30 of those days, 25 customers on 20 days, 35 customers on 30 days, 40 customers on 10 days, and 45 customers on 10 days. What is the variance of the number of Harry’s customers?
A. 30
B. 38
C. 59
D. 75
E. 83
7. What is the probability that exactly 1 out of 10 cars experience a breakdown if the probability of a breakdown is 30%?
A. .5121
B. .1211
C. .0282
D. .3828
E. .4276
8. An accounts receivable auditor is examining accounts for a client. The accounts receivable balance can be considered as a continuous random variable that exhibits normal distribution characteristics. The mean amount due per account is $5000. The standard deviation is $1000. The auditor selects an account at random.
The probability that the account selected by the Auditor has a balance which is outside of the range between $6500 and $7000 is:
A. .05
B. .10
C. 1.20
D. .96
E. .00
9. Suppose the length of time (in days) between sales for an automobile salesperson is modeled as an exponential distribution with a mean of 2 days. What is the probability the salesperson goes more than 5 days without a sale?
A. .75
B. .92
C. .08
D. .40
E. None of the above.
10. During lunch time, customers arrive at Joe’s Lunch counter according to a Poisson distribution with an average of 2 per 30 second period. What is the probability of having more than two arrivals in a two-minute period?
A. .9863
B. .9970
C. .0027
D .7619
E. None of the above
Use the following to answer questions 11-12
The new owner of a beauty shop is trying to decide whether to hire one, two, or three beauticians. She estimates that profits next year (in thousands of dollars) will vary with demand for her services and has estimated demand in three categories low, medium and high.
11. If she uses the optimistic criterion, how many beauticians will she decide to hire?
A. one
B. two
C. three
D. either one or two
E. either two or three
