Question

QUESTION 1

The optimal solution to an LP problem was  5.17 and  3.66. If  and  were restricted to be integers, then  = 5 and 4 will be a feasible solution, but not necessarily an optimal solution to the IP problem.

True

False

Question 2

A sample of 220 patients of a family medicine practice was surveyed two weeks after their doctor's visit to ask them whether the symptoms that prompted their visit improved, and whether they complied with the physician's treatment plan. The following table contains the results

	Symptoms improved	Symptoms did not improve
Complied	100	40
Did not comply	30	50

Of those in the sample whose symptoms did not improve, what percentage of them did not comply with the physician's treatment plan?

A. 62.5%

B. 44.4%

C. 55.6%

D. 22.7%

QUESTION 3

Suppose that 100 customers of an online retailer were asked in an email survey whether they preferred free 3-day shipping or whether they preferred overnight shipping for $4.99. 65% said that they preferred overnight shipping. 40% of the customers were male. 75% of the males preferred free 3-day shipping.

Suppose a randomly selected customer prefers free 3-day shipping. What is the probability the customer is a female?

A. 5%

B. 54%

C. 31%

D. 14%

QUESTION 4

Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by the utility function U(x) = ln(x+100,000). That is, if she loses $1,000, x = -1000.

If there is a 1% chance that the decision maker’s car, valued at $25,000, will be totaled during the next year, what is the most that she would be willing to (approximately) pay next year for an insurance policy that completely covers the potential loss?

Please round all results (also intermediate results which you use for further calculations!) to 2 decimals.

QUESTION 5

A promising college basketball talent has to decide whether or not to enter this year's NBA draft. If he enters, he expects that there is a 40% chance that he is a first round pick and a 60% chance that he is picked in a later round. As a first round pick, he would secure a 10 million dollar contract, if he is picked in a later round, his contract would only be worth $1 000 000.

If he does not enter the draft this year and continues to play in college, his chance of being a first round pick next year will increase to 60% (the contracts for first and later round picks are the same as in the previous year, $10 million and $1 000 000 respectively). However, there is a chance that he suffers a career ending injury next season, in which case he could make $50 000 as a coach in Europe.

Calculate the injury probability p (rounded to 2 decimals) that makes the decision maker indifferent between entering now and waiting until next year, that is for what probability are the EMV of both alternatives equal?

QUESTION 6

Since the median is the middle value of a data set, it must always be

	a.	larger than the mean
	b.	larger than the mode
	c.	smaller than the mean
	d.	None of the other answers are correct

Answer 1

Answer:

3.

65% said that they favored free 3-day transporting

40% of the clients were male.

75% of the guys favored free 3-day transporting

Presently,

absolute man who incline toward multi day dispatching = 0.4*0.75

= 0.3

absolute female who incline toward multi day dispatching = 0.65 - 0.30

= 0.35

P(female | incline toward multi day dispatching) = P(female and lean toward multi day delivering)/P(prefer multi day transporting) = 0.35/0.65

= 0.54

= 54%

Choice B is correct decision.

6.

Here the right alternative is Option D.

i.e.,

None of the other answers are right

Median is the value in the middle after the data has been arranged from smallest value to largest value,

Please post the remaining questions as separate post. Thank you.