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- From: Mathematics, Applied Mathematics
- Posted on: Tue 26 Jan, 2016
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Question 1
1. If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)
True
False
2 points
Question 2
1. Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.
True
False
2 points
Question 3
1. Probability trees are used only to compute conditional probabilities.
True
False
2 points
Question 4
1. 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
2 points
Question 5
1. The Hurwicz criterion is a compromise between the minimax and minimin criteria.
True
False
2 points
Question 6
1. The Hurwicz criterion is a compromise between the maximax and maximin criteria.
True
False
2 points
Question 7
1. The minimin criterion is optimistic.
True
False
2 points
Question 8
1. 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
2 points
Question 9
1. 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
2 points
Question 10
1. The chi-square test is a statistical test to see if an observed data fit a _________.
Normal probability distribution
continuous probability distribution
particular probability distribution
All of the above
2 points
Question 11
1. Determining the worst payoff for each alternative and choosing the alternative with the best worst is called
maximax
minimin
maximin
minimax
2 points
Question 12
1. 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:
Buy
Rent
Lease
All three tie.
2 points
Question 13
1. 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
2 points
Question 14
1. 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?
A1
A2
A3
Any of the above
2 points
Question 15
1. 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.
2 points
Question 16
1. 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.
2 points
Question 17
1. 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.
2 points
Question 18
1. Consider the following decision tree.
What is the expected value for the best decision? Round your answer to the nearest whole number.
2 points
Question 19
1. 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?
2 points
Question 20
1. 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?
2 points
Solution Description

Question 1

1. If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)

True

False

2 points

Question 2

1. Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.

True

False

2 points

Question 3

1. Probability trees are used only to compute conditional probabilities.

True

False

2 points

Question 4

1. 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

2 points

Question 5

1. The Hurwicz criterion is a compromise between the minimax and minimin criteria.

True

False

2 points

Question 6

1. The Hurwicz criterion is a compromise between the maximax and maximin criteria.

True

False

2 points

Question 7

1. The minimin criterion is optimistic.

True

False

2 points

Question 8

1. 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