Question (Category: Mathematics :General-Mathematics )
MAT 540 Probability trees are used only to compute conditional probabilities. bull Question 1 If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)bull Question 2 Probability trees are used only to compute conditional probabilities.bull Question 3 Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.bull Question 4 The minimax regret criterion maximizes the minimum regret.bull Question 5 The Hurwicz criterion is a compromise between the maximax and maximin criteria. bull Question 6 The Hurwicz criterion is a compromise between the minimax and minimin criteria.bull Question 7 Both maximin and minimin criteria are optimistic.bull Question 8Assume 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.bull Question 9The 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?bull Question 10A professor would like to utilize the normal distribution to assign grades such that 5% of students receive A39s. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)bull Question 11 The maximin criterion results in thebull Question 12Determining the worst payoff for each alternative and choosing the alternative with the best worst is calledbull Question 13A 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. WeatherCold Warm RainyS1 S2 S3 Bike: A1 10 8 6 Hike: A2 14 15 2 Fish: A3 7 8 9If the group chooses to minimize their maximum regret, what activity will they choose?bull Question 14A 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:bull Question 15A 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.bull Question 16A 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. bull Question 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).What is the numerical value of the minimax regret?bull Question 18A manager has developed a payoff table that indicates the profits associated with a set of alternatives under 2 possible states of nature. Alt S1 S21 10 22 -2 83 8 5What is the highest expected value? Assume that the probability of S2 is equal to 0.4.bull Question 19 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, what is the numerical maximum expected value?bull Question 20The 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?
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