Quiz 3 MAT500 / Quiz 3 MAT500

Question 1 
1. Probability trees are used only to compute conditional probabilities. 
Answer
True
False
2 points
Question 2 
Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed. 
Answer
True
False
2 points
Question 3 
If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)
Answer
True
False
2 points
Question 4 
The Hurwicz criterion is a compromise between the minimax and minimin criteria. 
Answer
True
False
2 points
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.
Answer
True
False
2 points
Question 6 
The equal likelihood criterion assigns a probability of 0.5 to each state of nature, regardless of how many states of nature there are. 
Answer
True
False
2 points
Question 7 
Both maximin and minimin criteria are optimistic.
Answer
True
False
2 points
Question 8 
The chi-square test is a statistical test to see if an observed data fit a _________.
Answer 
Normal probability distribution
continuous probability distribution
particular probability distribution
All of the above
2 points 
Question 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.
Answer 
0.1950
0.4772
0.4332
0.6247
2 points 
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.)
Answer 
80
83
90
93
2 points 
Question 11 
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:
\Answer 
Rent
Buy
Brisk
Slow
2 points 
Question 12 
The maximin criterion results in the
Answer 
minimum of the maximum payoffs
maximum of the maximum payoffs
maximum of the minimum payoffs
minimum of the minimum payoffs
2 points 
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
What is the conservative decision for this situation?
Answer 
A1
A2
A3
Any of the above
2 points 
Question 14 
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?
Answer 
A1
A2
A3
Any of the above
2 points 
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. 
Answer
2 points 
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. 
Answer
2 points 
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
2 points 
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. 
Answer
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 maximin?
Answer
2 points 
Question 20 
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?
Answer
2 points 

 

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