06 Jun MAT 540 Week 3 Quiz 2 Set 2 QUESTIONS NEW
Question 1 If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)
Question 2 Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.
Question 3 Probability trees are used only to compute conditional probabilities.
Question 4 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 5 The maximin approach involves choosing the alternative with the highest or lowest payoff.
Question 6 The Hurwicz criterion is a compromise between the minimax and minimin criteria.
Question 7 The Hurwicz criterion is a compromise between the maximax and maximin criteria.
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 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 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 Determining the worst payoff for each alternative and choosing the alternative with the best worst is called
Question 12 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 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
Question 14 The maximin criterion results in the
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 16 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 17 If the probability of brisk business is .40, what is the numerical maximum expected value?
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
Compute the expected value of perfect information assuming that the probability of S2 is equal to 0.4.
Question 19 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
Question 20 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?
Consider the following decision tree.
What is the expected value for the best decision? Round your answer to the nearest whole number.
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