MAT 540 Week 2
1. If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)
2. Probability trees are used only to compute conditional probabilities
3. Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed
4. The Hurwicz criterion is a compromise between the maximax and maximin criteria
5. The minimax regret criterion maximizes the minimum regret
6. The Hurwicz criterion is a compromise between the minimax and minimin criteria
7. The maximin approach involves choosing the alternative with the highest or lowest payoff.
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
9. 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
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. The maximin criterion results in the
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?
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
If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is
14. Determining the worst payoff for each alternative and choosing the alternative with the best worst is called
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? Write your anwsers with two places after the decimal
16. A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75? Round your answer to four places after the decimal
17. 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).
18. 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
19. Consider the following decision tree.
What is the expected value for the best decision? Round your answer to the nearest whole number
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
1. If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)
2. Probability trees are used only to compute conditional probabilities
3. Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed
4. The Hurwicz criterion is a compromise between the maximax and maximin criteria
5. The minimax regret criterion maximizes the minimum regret
6. The Hurwicz criterion is a compromise between the minimax and minimin criteria
7. The maximin approach involves choosing the alternative with the highest or lowest payoff.
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
9. 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
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. The maximin criterion results in the
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?
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
If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is
14. Determining the worst payoff for each alternative and choosing the alternative with the best worst is called
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? Write your anwsers with two places after the decimal
16. A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75? Round your answer to four places after the decimal
17. 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).
18. 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
19. Consider the following decision tree.
What is the expected value for the best decision? Round your answer to the nearest whole number
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
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