# MATHEMATICS

**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 [removed]

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 [removed]

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 [removed]

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 [removed]

2 points

**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 [removed]

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 [removed]

2 points