5.21 Kristina just won the lottery, and she must choose among three award options. She can elect to receive a lump sum today of $61 million, to receive 10 end-of-year payments of $9.3 million, or to receive 30 end-of-year payments of $5.4 million.

1. If she thinks she can earn 7% percent annually, which should she choose?
   -Select-She should accept the 30-year payment option as it carries the highest present value.She should accept the lump-sum payment option as it carries the highest present value.She should accept the 10-year payment option as it carries the highest present value.She should accept the lump-sum payment option as it carries the highest future value.Item 1

2. If she expects to earn 8% annually, which is the best choice?
   -Select-She should accept the lump-sum payment option as it carries the highest present value.She should accept the 30-year payment option as it carries the highest present value.She should accept the 10-year payment option as it carries the highest present value.She should accept the lump-sum payment option as it carries the highest future value.Item 2

3. If she expects to earn 9% annually, which option would you recommend?
   -Select-She should accept the lump-sum payment option as it carries the highest present value.She should accept the 30-year payment option as it carries the highest present value.She should accept the 10-year payment option as it carries the highest present value.She should accept the 30-year payment option as it carries the highest future value.Item 3

4. Explain how interest rates influence her choice.
   -Select-The higher the interest rate, the more valuable it is to get money rapidly.The lower the interest rate, the more valuable it is to get money rapidly.The higher the discount rate, the higher the more distant cash flows are valued.Interest rates do not influence the optimal choice in any way.Interest rates and the present value of cash flows are positively related.

5.21 Kristina just won the lottery, and she must choose among three award options. She can elect to receive a lump sum today of $61 million, to receive 10 end-of-year payments of $9.3 million, or to receive 30 end-of-year payments of $5.4 million.

1. If she thinks she can earn 7% percent annually, which should she choose?
   -Select-She should accept the 30-year payment option as it carries the highest present value.She should accept the lump-sum payment option as it carries the highest present value.She should accept the 10-year payment option as it carries the highest present value.She should accept the lump-sum payment option as it carries the highest future value.Item 1

2. If she expects to earn 8% annually, which is the best choice?
   -Select-She should accept the lump-sum payment option as it carries the highest present value.She should accept the 30-year payment option as it carries the highest present value.She should accept the 10-year payment option as it carries the highest present value.She should accept the lump-sum payment option as it carries the highest future value.Item 2

3. If she expects to earn 9% annually, which option would you recommend?
   -Select-She should accept the lump-sum payment option as it carries the highest present value.She should accept the 30-year payment option as it carries the highest present value.She should accept the 10-year payment option as it carries the highest present value.She should accept the 30-year payment option as it carries the highest future value.Item 3

4. Explain how interest rates influence her choice.
   -Select-The higher the interest rate, the more valuable it is to get money rapidly.The lower the interest rate, the more valuable it is to get money rapidly.The higher the discount rate, the higher the more distant cash flows are valued.Interest rates do not influence the optimal choice in any way.Interest rates and the present value of cash flows are positively related.

A hotel has 100 rooms. On any given night, it takes up to 105 reservations, because of the possibility of no-shows. Past records indicate that the number of daily reservations is uniformly distributed over the range 96-105. That is, each integer number in this range has a probability of 10%, of showing up. The no-shows are represented by the distribution in the table below.

Based on your thirty simulations, determine the following measures of performance of this booking system: the expected number of rooms used per night and the percentage of nights when more than 100 rooms are claimed. (Show your simulations and any other information used in the analysis. Don’t send any worksheet.)

Toss a fair coin repeatedly. Let N₁ be the number of tosses required to obtain heads followed immediately by tails. Let N₂ be the number of tosses required to obtain two heads in a row.

(A) Should N₁ and N₂ have the same expected value? If not, which expected value should be larger? Explain your answers.

(B) Find the probability mass function of N₁.

(C) Find the expected value of N₁.

(D) Find the probability mass function of N₂.

(E) Find the expected value of N₂.

Children laugh an average of 16.67 times an hour and adults laugh an average of 0.6667 times an hour. Let X be the number of times a child laughs in an hour, and let Y be the number of times an adult laughs in an hour.

c. Given that an adult laughs more than 1 time in an hour, what is the probability that the adult laughs at least 3 times in the next hour?

d. Given that an adult laughs less than 3 times in the next hour, what is the probability that the adult laughs once or less?

ThenumberofdailytextssentbyMarymountstudentsarenormally distributed with a mean of 80 texts and a standard deviation of 50 texts.

(a) Find the probability that a randomly selected Marymount student sends more than 100 texts each day.

(b) Find the probability that 25 randomly selected Marymount students will have a mean number of daily texts sent that is greater than 50 texts.

(c) Suppose a parent wants their child in the bottom 25% of texters. Find the cut-off value for the number of texts below which 25% of MCU students lie.

1. The number of raisins in buns has Poisson distribution with an average of 5 raisins per bun.

a) Bob buys a bun every day. What is the expected number of buns he buys before he finds a bun with no raisins at all?

b) Joe bought a bun for breakfast and cut it into two equal parts. What is the probability that at least one of these parts has no raisins in it?

c) Emily bought seven buns in the last month. What is the probability that fewer than two of these buns had at least three raisins in them?

a) The probability of the first serve is good for a tennis player is denoted by p. A player decides to increase p by taking a training program. After the training program completed, the player wishes to test Ho : p = 0.40 against HI : p > 0.40 . Let y be the number of first serve is good. Given that the total number of first serve, n = 20 and the critical region of the test is y 214} .

           i)          Determine the value of significance level, a for this test.

                   Find the probability of committing Type Il error if p = 0.65 .