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##### MAT540 Week 3 Discussion,all Quiz and Homework

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Question;? Question;1;2 out of 2 points;Probability trees are used only;to compute conditional probabilities.;? Question;2;2 out of 2 points;Seventy two percent of all;observations fall within 1 standard deviation of the mean if the data is;normally distributed.;? Question;3;2 out of 2 points;If two events are not mutually;exclusive, then P(A or B) = P(A) + P(B);? Question;4;2 out of 2 points;The Hurwicz criterion is a;compromise between the minimax and minimin criteria.;? Question;5;2 out of 2 points;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;6;2 out of 2 points;The minimin criterion is;optimistic.;? Question;7;2 out of 2 points;The equal likelihood criterion;assigns a probability of 0.5 to each state of nature, regardless of how many;states of nature there are.;? Question;8;2 out of 2 points;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;9;2 out of 2 points;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;10;2 out of 2 points;The chi-square test is a;statistical test to see if an observed data fit a _________.;? Question;11;2 out of 2 points;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?;? Question;12;2 out of 2 points;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;13;2 out of 2 points;The maximin criterion results in;the;? Question;14;2 out of 2 points;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;15;2 out of 2 points;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;2 out of 2 points;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;17;0 out of 2 points;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;18;2 out of 2 points;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?;? Question;19;2 out of 2 points;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 maximin?;? Question;20;2 out of 2 points;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?;Saturday, July 19, 2014 12:03:04 PM EDT;? Question;1;2 out of 2 points;If two events are not mutually;exclusive, then P(A or B) = P(A) + P(B);? Question;2;2 out of 2 points;Probability trees are used only;to compute conditional probabilities.;? Question;3;2 out of 2 points;Seventy two percent of all;observations fall within 1 standard deviation of the mean if the data is;normally distributed.;? Question;4;2 out of 2 points;The maximin approach involves;choosing the alternative with the highest or lowest payoff.;? Question;5;2 out of 2 points;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;6;2 out of 2 points;The Hurwicz criterion is a;compromise between the minimax and minimin criteria.;? Question;7;2 out of 2 points;The equal likelihood criterion;assigns a probability of 0.5 to each state of nature, regardless of how many;states of nature there are.;? Question;8;2 out of 2 points;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;9;2 out of 2 points;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;10;2 out of 2 points;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;11;2 out of 2 points;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;12;2 out of 2 points;The maximin criterion results in;the;? Question;13;2 out of 2 points;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;2 out of 2 points;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;15;2 out of 2 points;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;2 out of 2 points;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;2 out of 2 points;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?;? Question;18;2 out of 2 points;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;19;2 out of 2 points;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;20;2 out of 2 points;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 maximin?;? Question;1;2 out of 2 points;Seventy two percent of all;observations fall within 1 standard deviation of the mean if the data is;normally distributed.;? Question;2;2 out of 2 points;Probability trees are used only;to compute conditional probabilities.;? Question;3;2 out of 2 points;If two events are not mutually;exclusive, then P(A or B) = P(A) + P(B);? Question;4;2 out of 2 points;The Hurwicz criterion is a;compromise between the maximax and maximin criteria.;? Question;5;2 out of 2 points;The maximin approach involves;choosing the alternative with the highest or lowest payoff.;? Question;6;2 out of 2 points;The Hurwicz criterion is a;compromise between the minimax and minimin criteria.;? Question;7;2 out of 2 points;The equal likelihood criterion;assigns a probability of 0.5 to each state of nature, regardless of how many;states of nature there are.;? Question;8;2 out of 2 points;The chi-square test is a;statistical test to see if an observed data fit a _________.;? Question;9;2 out of 2 points;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;2 out of 2 points;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;2 out of 2 points;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;12;0 out of 2 points;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;2 out of 2 points;Determining the worst payoff for;each alternative and choosing the alternative with the best worst is called;? Question;14;2 out of 2 points;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;15;2 out of 2 points;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;2 out of 2 points;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;17;2 out of 2 points;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 maximin?;? Question;18;2 out of 2 points;Consider the following decision;tree.;What is the expected value for the best decision? Round your;answer to the nearest whole number.;? Question;19;2 out of 2 points;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?;? Question;20;0 out of 2 points;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 1;2 out of 2 points;Probability trees are used only to compute conditional probabilities.;Question 2;2 out of 2 points;If two events are not mutually exclusive, then P(A or B) =;P(A) + P(B);Answer;Question 3;2 out of 2 points;Seventy two percent of all observations fall within 1;standard deviation of the mean if the data is normally distributed.;Question 4;2 out of 2 points;The Hurwicz;criterion is a compromise between the maximax and maximin criteria.;Question 5;2 out of 2 points;The maximin approach involves choosing the alternative with;the highest or lowest payoff.;Question 6;2 out of 2 points;The minimin criterion is optimistic.;Question 7;2 out of 2 points;Both maximin and minimin criteria are optimistic.;Question 8;2 out of 2 points;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.);2 out of 2 points;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;2 out of 2 points;The chi?square test is a statistical test to see if an;observed data fit a _________.;Question 11;2 out of 2 points;The maximin criterion results in the;Question 12;2 out of 2 points;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?;A3;Question 13;2 out of 2 points;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;2 out of 2 points;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;2 out of 2 points;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;2 out of 2 points;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;2 out of 2 points;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;2 out of 2 points;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;2 out of 2 points;Consider the following decision tree.;What is the expected value for the best decision? Round your;answer to the nearest whole number.;Question 20;2 out of 2 points;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 1;2 out of 2 points;Seventy two percent of all;observations fall within 1 standard deviation of the mean if the data is normally;distributed.;Question 2;2 out of 2 points;Probability trees are used only;to compute conditional probabilities.;Question 3;2 out of 2 points;If two events are not mutually;exclusive, then P(A or B) = P(A) + P(B);Question 4;2 out of 2 points;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;2 out of 2 points;Both maximin and minimin criteria;are optimistic.;Question 6;0 out of 2 points;The Hurwicz criterion is a;compromise between the maximax and maximin criteria.;Question 7;2 out of 2 points;The maximin approach involves;choosing the alternative with the highest or lowest payoff.;Question 8;2 out of 2 points;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;2 out of 2 points;The chi-square test is a;statistical test to see if an observed data fit a _________.;Question 10;2 out of 2 points;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 11;2 out of 2 points;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 12;0 out of 2 points;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?;Question 13;2 out of 2 points;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;Lease;Question 14;2 out of 2 points;Determining the worst payoff for;each alternative and choosing the alternative with the best worst is called;Question 15;2 out of 2 points;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;2 out of 2 points;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 17;0 out of 2 points;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 maximin?;Question 18;2 out of 2 points;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 19;0 out of 2 points;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?;Evaluation Method Correct;Answer Case Sensitivity;Exact Match 57;Question 20;0 out of 2 points;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 1;2 out of 2 points;| Probability trees are used only to compute conditional;probabilities.;* Question 2;2 out of 2 points;| If two events are not mutually exclusive, then P(A or B) =;P(A) + P(B);Answer;* Question 3;2 out of 2 points;| Seventy two percent of all observations fall within 1;standard deviation of the mean if the data is normally distributed.;Answer;* Question 4;2 out of 2 points;| The equal likelihood criterion assigns a probability of;0.5 to each state of nature, regardless of how many states of nature there are.;* Question 5;2 out of 2 points;| The maximin approach involves choosing the alternative;with the highest or lowest payoff.;* Question 6;2 out of 2 points;| 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 7;0 out of 2 points;| The Hurwicz criterion is a compromise between the minimax;and minimin criteria. Week 3 Discussion 1Discuss SimulationSelect one (1) of the following topics for;your primary discussion posting:?Identify the part of setting up a;simulation in Excel that you find to be the most challenging, and explain why.;Identify resources that can help you with that.?Explain how simulation is used in the real;world. Provide a specific example from your own line of work, or a line of work;that you find particularly interesting.MAT540Week;3 HomeworkChapter 14 1. The Hoylake Rescue Squad receives an emergency call every 1, 2, 3;4, 5, or 6 hours, according to the following probability distribution. The;squad is on duty 24 hours per day, 7 days per week;Time Between;Emergency Calls (hr.);Probability;1;0.05;2;0.10;3;0.30;4;0.30;5;0.20;6;0.05;1.00;a.;Simulate the emergency calls for 3 days (note that this will require a;?running?, or cumulative, hourly clock), using the random number table.b.;Compute the average time between calls and compare this value with the;expected value of the time between calls from the probability distribution. Why;are the results different?2. The time between arrivals of cars at the Petroco Service Station;is defined by the following probability distribution;Time Between;Arrivals (min.);Probability;1;0.15;2;0.30;3;0.40;4;0.15;1.00;a.;Simulate the arrival of cars at the service station for 20 arrivals and;compute the average time between arrivals.b.;Simulate the arrival of cars at the service station for 1 hour, using a;different stream of random numbers from those used in (a) and compute the;average time between arrivals.c.;Compare the results obtained in (a) and (b).3. The Dynaco Manufacturing Company produces a product in a process;consisting of operations of five machines. The probability distribution of the;number of machines that will break down in a week follows;Machine Breakdowns;per Week;Probability;0;0.10;1;0.10;2;0.20;3;0.25;4;0.30;5;0.05;1.00;a.;Simulate the machine breakdowns per week for 20 weeks.b.;Compute the average number of machines that will break down per week.5. Simulate the decision situation described in Problem 16(a) at the;end of Chapter 12 for 20 weeks, and recommend the best decision.Reference Problem 16(a) in Chapter 12: A concessions manager at the Tech versus;A&M football game must decide whether to have the vendors sell sun visors;or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and;a 55% chance of sunshine, according to the weather forecast in College;Junction, where the game is to be held. The manager estimates that the;following profits will result from each decision, given each set of weather;conditions;Weather Conditions;Decision;Rain;Overcast;Sunshine;.30;.15;.55;Sun visors;$-500;$-200;$1,500;Umbrellas;2,000;0;-900;a. Compute the expected value;for each decision and select the best one.6. Every time a machine breaks down at the;Dynaco Manufacturing Company (Problem 3), either 1, 2, or 3 hours are required;to fix it, according to the following probability distribution;Repair Time (hr.);Probability;1;0.30;2;0.50;3;0.20;1.00;a.;Simulate the repair time for 20 weeks and then compute the average weekly;repair time.;="msonormal">="msonormal">

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