Probability questions

(PLEASE SHOW CALCULTIONS)

2. 

A calculus instructor uses computer aided instruction and allows
students to take the midterm exam as many times as needed until a
passing grade is obtained.  Following is a record of the number of
students in a class of 20 who took the test each number of times.

                                   

Students   Number of tests

     

10   1

7   2

2   3

1   4

Compute the variance.

(Points: 2)



3. 

A process follows the binomial distribution with n = 8 and p = .3. 
Find

P(x > 6) to 4 decimal places  --   x. x x x x

(Points: 2)



4. 

Assume that the time required to download a file from the Internet is
exponentially distributed with mean equal to 4 minutes.  What is the
probability that a download will require at least 2 but not more than 4
minutes?  (to five decimal places  ---   0.xxxxx)

(Points: 2)



5. In a multicriteria decision problem (Points: 1)

it is impossible to select a single decision alternative

the decision maker must evaluate each alternative with respect to each
criterion

successive decisions must be made over time

each of the above is true

6. 

The first step in problem solving is

(Points: 1)

determination of the correct analytical solution procedureP>

definition of decision variables

the identification of a difference between the actual and desired state
of affairs

implementation

7. 

The terms ‘stochastic’ and ‘deterministic’ have the same meaning
in quantitative analysis.

(Points: 1)

True

False

8. 

The most successful quantitative analysis will separate the analyst from
the managerial team until after the problem is fully structured.

(Points: 1)

True

False

9. 

The relationship d = 5000 - 25p describes what happens to demand (d) as
price (p) varies.  Here, price can vary between $10 and $50.

How many units can be sold at the $10 price? 

(Points: 1)

3750

4750

2750

5750

10. 

There is a fixed cost of $50,000 to start a production process.  Once
the process has begun, the variable cost per unit is $25.  The revenue
per unit is projected to be $45.

Find the break-even point.

(Points: 1)

2850

3000

2500

3500

11. 

A small firm builds television antennas.  The investment in plan and
equipment is $200,000.  The variable cost per television antenna is
$500.  The price of the television antenna is $1000.  How many
television antennas would be needed for the firm to break even?

(Points: 1)

400 television antennae

600 television antennae

200 television antennae

650 television antennae

12. 

In the set of all past due accounts, let the event A mean the account is
between 31 and 60 days past due and the event B mean the account is that
of a new customer.  The complement of A is

(Points: 1)

all new customers

all accounts fewer than 31 or more than 60 days past due

all accounts from new customers and all accounts that are from 31 to 60
days past due

all new customers whose accounts are between 31 and 60 days past due

13. 

If P(AB) = 0

(Points: 1)

A and B are independent events>

P(A) + P(B) = 1

A and B are mutually exclusive events

either P(A) = 0 or P(B) = 0

14. 

When assigning subjective probabilities, use experience, intuition, and
any available data.

(Points: 1)

True

False

15. 

There are two more assignments in a class before its end, and if you get
an A on at least one of them, you will get an A for the semester.  Your
subjective assessment of your performance is

 

              Event Probability

A on paper and A on exam .25

A on paper only .10

A on exam only .30

A on neither .35

What is the probability of getting an A in the course?

(Points: 1)

.45

.55

.65

.75

16. 

A medical research project examined the relationship between a
subject’s weight and recovery time from a surgical procedure, as shown
in the table below.

 

  Underweight Normal weight Overweight

Less than 3 days 6 15 3

3 to 7 days 30 95 20

Over 7 days 14 40 27

Given that recovery takes over 7 days, what is the probability the
patient is overweight?

(Points: 1)

73/200 =.365

200/146=1.37

146/200 = .73

27/81=.333

17. 

It is estimated that 3% of the athletes competing in a large tournament
are users of an illegal drug to enhance performance.  The test for this
drug is 90% accurate.  What is the probability that an athlete who
tests positive is actually a user?

(Points: 1)

.2177

.7823

.10885

.4354

18. 

Experiments with repeated independent trials will be described by the
binomial distribution if

(Points: 1)

the trials are continuous

each trial result influences the next

the time between trials is constant

each trial has exactly two outcomes whose probabilities do not change>

19. 

When the exponential distribution probability is given as

                                P(x  9
) = 1 - e-9/18

the average value for x is

(Points: 1)

18

9

9/18

1/2

20. 

The weight of an object, measured to the nearest gram, is an example of

(Points: 1)

a continuous random variable

a discrete random variable

either a continuous or a discrete random variable, depending on the
weight of the object

either a continuous or a discrete random variable depending on the
units of measurement

21. 

Z is a standard normal random variable.  The P(z > 2.11) equals

(Points: 1)

0.4821

0.9821

0.5

0.0174

22. 

Suppose that the arrival time for the next bus at a bus stop is
uniformly distributed between 1 and 25 minutes.  The probability that
the bus will arrive within the next 5 minutes is 1/5.

(Points: 1)

True

False

23. 

If the Poisson distribution describes the number of occurrences per
interval, the exponential distribution describes the length of the
interval between occurrences.

(Points: 1)

True

False

24. 

Sensitivity analysis considers

(Points: 1)

how sensitive the decision maker is to risk

changes in the number of states of nature

changes in the values of the payoffs

changes in the available alternatives

25. 

If P(high) = .3, P(low) = .7, P(favorable | high) = .9, and
P(unfavorable | low) = .6, then P(favorable) =

(Points: 2)

.10

.27

.30

.55

26. 

The probability distribution of the possible payoffs associated with a
decision alternative or a decision strategy is the

(Points: 1)

risk profile

expected value of sample information

influence diagram

payoff table

27. The expected value of an alternative can never be negative.
(Points: 1)

True

False

28. 

The table shows both prospective profits and losses for a company,
depending on what decision is made and what state of nature occurs. 
Use the information to determine what the company should do

if minimax regret is the strategy.

               

  s1 s2 s3

d1 30 80 -30

d2 100 30 -40

d3 -80 -10 120

d4 20 20 20

 

(Points: 1)

d1

d2

d3

d4



 

29. 

A payoff table is given as

 

  s1 s2 s3

d1 250 750 500

d2 300 -250 1200

d3 500 500 600

The probability of each state is .2  .4  and .4  in order.

What is the EVPI?

(Points: 2)

925

240

695

330

30. The focus of smoothing methods is to smooth (Points: 1)

the irregular component

wide seasonal variations

significant trend effects

long range forecasts

31. 

Linear trend is calculated as Tt = 28.5 + .75t.  The trend projection
for period 15 is

(Points: 1)

11.25

28.50

39.75

44.25

32. 

A qualitative forecasting method that obtains forecasts through "group
consensus" is known as the

(Points: 1)

Autoregressive model

Delphi approach

mean absolute deviation

None of these alternatives is correct

33. 

One measure of the accuracy of a forecasting model is the

(Points: 1)

smoothing constant

trend component

mean absolute deviation

seasonal index

34. 

Quantitative forecasting methods do not require that patterns from the
past will necessarily continue in the future.

(Points: 1)

True

False

35. 

All quarterly time series contain seasonality.

(Points: 1)

True

False

36. A four-period moving average forecast for period 10 would be found
by averaging the values from periods 10,9, 8, and 7. (Points: 1)

True

False

37. 

If the random variability in a time series is great, a high value should
be used to exponentially smooth out the fluctuations.

(Points: 1)

True

False

38. 

Use a four period moving average to forecast attendance at baseball
games.  Historical records show

                                5346,
7812, 6513, 5783, 5982, 6519, 6283, 5577, 6712, 7345

 

THE FORECAST FOR PERIOD 11 is?

(Points: 1)

6272.75

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                                508, 490,
502, 505, 493, 506, 492, 490, 503, 501

                Do the scores support an increasing or a
decreasing trend?

(Points: 1)

increasing

decreasing