QMB3600 cumulative final exam

This document is for review purposes and does not represent every type of problem that may be on the 40 question QMB3600 cumulative final exam.

1.         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 ffeels 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     answerto 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

18.       A statistician working for a car manufacturer developed a statistical model for       predicting delivery time (the number of days between ordering a car and actual         delivery) of a particular model for which there is a range of factory-fitted options.  Use            the output below to forecast the difference in delivery times for cars with 6 options and     9 options, rounded to two decimal places.

 A.       4.38

 B.       3.28

 C.       6.58

 D.       9.84

 E.        29.73

19.       Given the table below what is the MAD and the MSE?

MAD = ___________________     MSE = ___________________________

20.       The Acme Computer Company has recorded sales of one of its products for a six-week period:  Using the three-week simple moving-average method, forecast sales for week 7.

A.        20

B.        21

C.        22

D.        23

F.         24

21.     Shown below are data that reflect the number of daily traffic accidents at a dangerous city intersection. The regression equation is: number of accidents = 5.3 + 0.5 t

          What is the forecasted number of accidents for day 6?

                    Day (t)           number of accidents

                           1                     5       

                           2                      7    

                           3                     8

                           4                      6

                           5                      8

A.        8.0

B.        5.8

C.        8.3

D.        0.6

E.         9.0

22.  The following table contains the number of consumer complaints received in a Publix supermarket in Florida.  Use exponential smoothing with a constant of α = 0.33 to forecast the number of complaints in March, round to the nearest whole number of complaints.

A.        39

B.        42

C.        45

D.        53

E.         64

For the next 3 questions, consider the following summary output from Microsoft Excel for a simple regression of Halliburton (ticker symbol HAL) weekly stock prices on the S&P500 stock index, for the period January 2004 through August 2006.

23.    According to the regression model, the correlation between Halliburton’s stock price and the S&P500 index value is:

24.     The regression model ABOVE is:

25.    According to the regression model ABOVE, when the S&P 500 index value is 1,000, the forecasted Halliburton stock price is:

26.    Corporate AAA bond interest rates for 12 consecutive months are 9.5%, 9.3%, 9.4%, 9.6%, 9.8%, 9.7%, 9.8%, 10.5%, 9.9%, 9.7%, 9.6% and 9.6%. The three-month weighted moving average forecast (with weights 0.2, 0.4 and 0.4 – from oldest to most recent respectively) for the next month, rounded to two decimal places, is:

A.           9.60%

B.           9.65%

C.           9.70%

D.           9.62%

E.           None of the above.

Questions 27 & 28 apply to this information: Quill Manufacturing Business makes two models of marking pens. An unlabeled graph for this problem and the requirements for each lot of pens in the three manufacturing departments are given below. All three departments are necessary in the production of both types of pens. The profit for either kind of pen is $1000 per lot.  An unlabeled graph for this problem is given below. The dotted line represents the objective function line.

27.       What is the optimal production quantity of the Fliptop model?

30.       The Quiet Meadow Studio sells photographs and prints.  It cost $20 to purchase each photograph and it takes 2 hours to frame it.  It costs $25 to purchase each print and it takes 5 hours to frame it.  The store has at most $400 to spend and   at most 60 hours to frame. 
It makes $30 profit on each photograph and $50 profit on each print. Determine the maximum profit.

s.t.

           A + 2 B + 3 C + 3 D <   15000            Print

        2 A + 4 B +   C + 3 D <   20000            Cut

        3 A + 2 B + 5 C + 3 D <   20000            Fold

        A >   1000                                               Print A

        B >   1000                                               Print B

        C >   1000                                               Print C

31.       Answer the following question using the Excel output above. Which constraint(s) are binding?

33.       Quentin Magic Brown manufactures sports shoes and wants to maximize the company’s profits. The company makes two types of sport shoe, Airwalkers and Bouncy Basketball shoes.  The company earns $10 profit on each pair of Airwalkers and $18 profit on each pair of Bouncy Basketball shoes.
The manufacturing process includes cutting the materials on a machine and having workers assemble the pieces.  Each pair of Airwalkers requires 3 minutes of cutting time and the Bouncy Basketball shoes require 2 minutes. The machines that cut the material can run at most 1200 minutes a week.
Each worker takes 7 hours to assemble a pair of Airwalkers and 8 hours to assemble a pair of Bouncy Basketball shoes; the maximum number of hours available is 3500 per week. 
Determine the maximum profit for this problem? 

A.        $3200

B.        $4000

C.        $4280

D.        $6295

E.         $7875

Questions 34-37 apply to the Excel output for the Quantum Mo-Botics model is below. The company makes three types of machines and has limitations with regards to the amount of skilled and unskilled labor hours available and time on the assembly line.

MAX Profit = 800SemiAuto+1000Robotic + 500Manual

s.t.

                         30SemiAuto + 100Robotic + 45Manual < 4500  Skilled Labor

                        100SemiAuto + 70Robotic + 90Manual  < 9000  Unskilled Labor

                         15SemiAuto +  20Robotic + 10Manual  < 2000  Assembly Line

36.       Answer the following question using the Excel output above. Keeping within the confines of the problem, how many more hours of skilled workers could you add to the      department?

37.       Using the Excel output above, how much is each additional unit of unskilled labor worth?