mat 540 3 mulitple choice questions
 Let’s say that 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 72 years and a standard deviation of 5 years. What proportion of the plan participants are expected to survive to see their 75^{th}
birthday? Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal.
2. Mr. Sartre is considering four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

Economic Conditions 

Poor (S1) 
Average (S2) 
Good (S3) 
Excellent (S4) 

A 
38 
25 
33 
10 
B 
10 
15 
20 
85 
C 
20 
100 
20 
25 
D 
25 
25 
100 
25 
Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Note: Report your answer as an integer, rounding to the nearest integer, if applicable
3. Klein Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows:

Cost/oz 
protien (%) 
fat (%) 
Partner’s Choice 
$0.20 
45 
20 
Feline Excel 
$0.15 
15 
30 
Klein Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Note: Please write your answers with two significant places after the decimal and do not include the dollar “$” sign. For instance, $9.45 (nine dollars and fortyfive cents) should be written as 9.45