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 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

 

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

 

 

Month                 Number of Complaints

January                               36

February                             45

March                                 81

April                                   90

May                                  108

June                                  144

	Df

A.  Positive.

B.  Negative.

C.  Significant and either positive or negative.

D.  Significant, but it cannot be determined whether the correlation is positive or negative.

E.  Not significant.

A.  Not significant, because the standard error of the intercept is high compared to the

standard error of the independent variable.

B.  Significant at the 0.01 level, because the coefficient of determination is less than 0.05.

C.  Significant at the 0.05 level, because the p-value is less than 0.05.

D.  Not significant, because the coefficient of determination is larger than 1.0.

E.  Significant at the 0.01 level, because the t-statistic is negative.

A.        $29.75/share.

B.        $0.35/share.

C.        $122/share.

D.        $121.65/share.

E.        Cannot be determined from the tabulated data.

 

 

The S&P index value must be ________ for the Halliburton stock to be priced at $24.75

			Available production hrs.

A.        5 lots

B.        4 lots

C.        2 lots

D.        7 lots

E.        6 lots

28.       If all the constraint inequalities in the original problem were ≥, then the following is true:

 

A.        The value of the objective function at the optimum solution is zero

B.        There will be multiple optimal solutions

C.        The problem will become unbounded

D.        The problem has a unique solution

E.        None of the above is true

 

 

 

29.       Let M be the number of units to make and B be the number of units to buy of a certain            product. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the    objective function of the LP model to minimize the cost of      production would be,

A.        Min 4000 (M + B)

B.        Max 8000M + 12000B

C.        Min 2M + 3B

D.        Max 2M + 3B

E.        Min 4000U -2M-3B

 

A.        360

B.        600

C.        700

D.        740

E.        800

 

 

Questions 31 & 32 apply to this information:  Quality Bike Maps has produced four map designs for the local area. A limited amount of time (in minutes) is allocated to the printing, cutting and folding of each map. Additionally, at least one thousand of map designs A, B, and C must be printed.  The profit per map is $1 for A and B and $2 for C and D.  The Excel output is provided below. 

Max Profit = A + B + 2 C + 2 D

Microsoft Excel 14.0 Sensitivity Report
	Objective Function Value  $10,166.67
Variable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$B$18	Map A	1500	0	1	1	0.333333333
	$C$18	Map B	1000	0	1	0.333333333	1E+30
	$D$18	Map C	1000	0	2	0.333333333	1E+30
	$E$18	Map D	2833.333333	0	2	1	0.5
Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$B$24	Print	15000	0.5	15000	1000	5666.666667
	$B$25	Cut	16500	0	20000	1E+30	3500
	$B$26	Fold	20000	0.166666667	20000	7000	1000
	$B$27	Print A	1500	0	1000	500	1E+30
	$B$28	Print B	1000	-0.33333333	1000	1750	1000
	$B$29	Print C	1000	-0.33333333	1000	500	1000

A.        Print and Fold

B.        Cut and Print A

C.        Print B and Print C

D.        Print and Cut

E.        Print, Fold, Print B and Print C

 

32.       Answer the following question using the Excel output above. Keeping within the confines of the problem, the profit on Map A has increased by one dollar.  Determine the new objective function value.

 

A.        1,500

B.        11,166.67

C.        11,500.67

D.        11,666.67

E.        12,566.67

 

Microsoft Excel 14.0 Sensitivity Report
Objective Function Value			$ 82,025.32
Variable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$B$18	SemiAuto	74.05063291	0	800	628.5714286	432.4786325
	$C$18	Robotic	22.78481013	0	1000	1666.666667	440
	$D$18	Manual	0	-320.253164	500	320.2531646	1E+30
Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$B$24	Skilled labor	4500	5.569620253	4500	3605.263158	1800
	$B$25	Unskilled labor	9000	6.329113924	9000	3805.555556	5850
	$B$26	Assembly line	1566.455696	0	2000	1E+30	433.5443038

34.       Answer the following question using the Excel output above, determine the new objective function value if the profit on the second variable, Robotic, increases by $1000?

 

A.        $22,785.00

B.        $19,125.64

C.        $33,800.00

D.        $102,805.32

E.        $104,810.32

 

35.       Answer the following question using the Excel output above. Keeping within the confines of the problem, you are required to hire a full time (40 hours) person who is qualified to work in any department. Select the constraint where you will gain the most profit and determine the additional profit to be gained?

 

A.        $253.16

B.        $222.80

C.        $341.00

D.        $129.50

E.        $119.50

 

 

A.        2875.33

B.        1280.56

C.        1550.56

D.        3805.56

E.        3605.26

 

 

A.        $74.500

B.        $22.790

C.        $5.570

D.        $6.329

E.        $3.250

 

38.              An ice cream plant make’s Chocolate and Strawberry ice cream.

There is $40 profit for a case of Chocolate and $32 for a case of Strawberry and has the following constraints:

 

                        32C + 8S   < 4,800     Flavoring

                        28C + 32S < 14,000   Coloring

 

 

a. What is the optimal solution?

b. Now add a constraint: demand for Strawberry is always less than 200 cases and determine the optimal solution.

c. Add another constraint: demand for Chocolate is always less than 400 cases and determine the optimal solution.

 

 

 

 

39.       Using the decision table below

a. Determine the expected value for the best decision

b. Determine the most you would pay for a highly reliable forecast.

	0.2	0.7	0.1
	S1	S2	S3
D1	500	300	-400
D2	600	200	200
D3	-100	-300	900

 

 

 

 

 

 

40.       In a survey about soft drinks it was found that 5% of the respondents like diet soft drinks. 

12% of them liked the brand Coke.  Of all the Diet soda drinkers 40% liked Coke.

a. What is the probability that a respondent like Coke and Diet drinks?

b. What is the probability that the respondent like Diet or not Coke?

c. Of the people who did not like diet drinks what is the probability that that liked Coke?