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MATH 540 WEEK 2 QUIZ 2

Question 1 1.Probability trees are used only to compute conditional probabilities. True False Question 2 If two events are not mutually exclusive, then P(A or B) = P(A) + P(B) True False Question 3 Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed. True False Question 4 The Hurwicz criterion is a compromise between the maximax and maximin criteria. True False 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. True False Question 6 The Hurwicz criterion is a compromise between the minimax and minimin criteria. True False 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. True False 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. 0.1950 0.4772 0.4332 0.6247 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? 0.0228 0.0475 0.0485 0.0500 Question 10 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.) 80 83 90 93 Question 11 Determining the worst payoff for each alternative and choosing the alternative with the best worst is called maximax minimin maximin minimax 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. If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is: 12 55 57 69 Question 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? A1 A2 A3 Any of the above 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 maximax strategy is: Rent Buy Brisk Slow 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 Consider the following decision tree. What is the expected value for the best decision? Round your answer to the nearest whole number. Answer  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 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 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).


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