MAT 540 QUIZ 2

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MAT 540 Quiz 2

1.     Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed. 

2.     Probability trees are used only to compute conditional probabilities.

3.     If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)

4.     The maximin approach involves choosing the alternative with the highest or lowest payoff.

5.     The Hurwicz criterion is a compromise between the maximax and maximin criteria.

6.     Both maximin and minimin criteria are optimistic.

7.     The minimin criterion is optimistic.

8.     Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot.  Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot.

9.     A professor would like to utilize the normal distribution to assign grades such that 5% of students receive A's.  If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)

10.   The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport.  At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels.  What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels?

11.   Determining the worst payoff for each alternative and choosing the alternative with the best worst is called

12.   The maximin criterion results in the

13.   A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in.  Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.                   

                        Weather
                  Cold    Warm  Rainy
                  S1      S2               S3
Bike:   A1      10          8           6
Hike:  A2      14        15           2
Fish:   A3        7          8           9

If the group chooses to minimize their maximum regret, what activity will they choose?

14.   A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

           

If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is:

15.   A life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 71 years and a standard deviation of 3.5 years. What proportion of the plan participants are expected to see their 75th birthday? Note: Write your answers with two places after the decimal, rounding off as appropriate. 

16.   A brand of television has a lifetime that is normally distributed with a mean of 7 years and a standard deviation of 2.5 years. What is the probability that a randomly chosen TV will last more than 8 years? Note: Write your answers with two places after the decimal, rounding off as appropriate. 

17.   A manager has developed a payoff table that indicates the profits associated with a set of alternatives under 2 possible states of nature.

            Alt       S1           S2
            1          10             2
            2          -2              8
            3            8             5

What is the highest expected value? Assume that the probability of S2 is equal to 0.4.

18.   A manager has developed a payoff table that indicates the profits associated with a set of alternatives under 2 possible states of nature.

            Alt       S1           S2
            1          10             2
            2          -2              8
            3            8             5
Compute the expected value of perfect information assuming that the probability of S2 is equal to 0.4.

19.   The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).

           

What is the numerical value of the maximin?

20.   A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

           

If the probability of brisk business is .40, what is the numerical maximum expected value?