MAT 540 Quiz 2. 20/20. Get an A++. - 63157

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Question 1

Probability trees are used only to compute conditional probabilities.

 

Question 2

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

 

Question 3

Seventy two percent of all observations fall within 1 standard deviation of the mean if the data

is normally distributed.

 

Question 4

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

 

Question 5

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

 

Question 6

The minimin criterion is optimistic.

 

Question 7

Both maximin and minimin criteria are optimistic.

 

Question 8

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.)

 

Question 9

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 10

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

 

Question 11

The maximin criterion results in the

 

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

What is the conservative decision for this situation?

 

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 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 maximin strategy is:

 

Question 15

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 16

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 17

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 probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4,

and 0.4, respectively what is the EVPI for this situation?

 

Question 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

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

 

Question 19

Consider the following decision tree.

What is the expected value for the best decision? Round your answer to the nearest whole

number.

 

Question 20

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?

 
Solution Description

Question 1

Probability trees are used only to compute conditional probabilities.

 

Question 2

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

 

Question 3

Seventy two percent of all observations fall within 1 standard deviation of the mean if the data

is normally distributed.

 

Question 4

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

 

Question 5

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

 

Question 6

The minimin criterion is optimistic.

 

Question 7

Both maximin and minimin criteria are optimistic.

 

Question 8

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? (R

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