MAT540 - Quiz 2 - A Graded Solution - 41122

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•             Question 1

               

 

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

                                               

•             Question 2

               

 

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

                                               

•             Question 3

               

 

Probability trees are used only to compute conditional probabilities.

•             Question 4

               

                The minimin criterion is optimistic.

                                               

•             Question 5

               

                Using the minimax regret criterion, we first construct a table of regrets. Subsequently, for each possible decision, we look across the states of nature and make a note of the maximum regret possible for that decision. We then pick the decision with the largest maximum regret.

                                               

•             Question 6

               

 

Both maximin and minimin criteria are optimistic.

                                               

•             Question 7

               

                The equal likelihood criterion assigns a probability of 0.5 to each state of nature, regardless of how many states of nature there are.

•             Question 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.

                               

                                               

•             Question 9

               

                The chi-square test is a statistical test to see if an observed data fit a _________.

                               

                                               

•             Question 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?

                               

               

•             Question 11

               

 

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.

                                               

•             Question 12

               

 

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?

                               

•             Question 13

               

 

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.

The maximax strategy is:

                               

                                                                               

•             Question 14

               

 

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

 

What is the conservative decision for this situation?

                                               

•             Question 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. 

 

               

•             Question 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.

                                               

•             Question 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.

               

•             Question 18

               

                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 minimax regret?

 

                               

                                               

•             Question 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?

 

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

 

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