Humans are known to have a mean gestation period of 280 days (from last menstruation) with a standard deviation of about 9 days. A hospital wondered whether there was any evidence that their patients were at risk for giving birth prematurely. In a random sample of 70 women, the average gestation time was 277.7 days. Is the alternative hypothesis one-sided or two-sided? (type your choice as either one-sided or two-sided) What is the value of the test statistic? (round to 3 decimal places) What is the P-value of the test? (round to 3 decimal places) What is the conclusion of the test if alpha is 0.05? (type your choice as either reject or fail to reject)

You are saving for the college education of your two children. They are two years apart in age: one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be 21,000$ per year per child, payable at the beginning of each school year. It takes four years to graduate. The annual interest is 15%. How much money must you deposit in an account each year to fund your children’s education? Your deposits begin now. You will make your last deposit one year before your oldest child enters college.

Homework Problem 18_1

An analysis of HL Corporation suggests that in the next year the price of its stock will be either $50 or $30. The current price is $40. The 1-year riskless rate is 10%.

Consider a call option that expires in one year with an exercise price of $35.

a) The Replicating Portfolio is a portfolio of stocks and bonds that exactly replicates the payoff of the call option under all conditions, in this case the two states.

What portfolio of stocks (number of shares bought or shorted) and bonds (dollars borrowed/shorted or lent/long) that has same payoff if this Call option?

b) What is the fair value of this call? and why?

c) Create a riskless hedge with the call and stock. A riskless hedge is a portfolio of stocks and calls that have the same payoff in all conditions, in this case the two states.

For example, Write 1 calls and buy .75 shares or Buy 1 call and short .75 shares.

d) An arbitrage is a strategy that has all positive cash flows with no investment or negative cash flows.

How would you create an arbitrage if the Call were priced at $15?

e) How would you create an arbitrage if the Option were priced at $5?

If an investor purchases shares in a no-load mutual fund for $28 and after seven years the shares appreciate to $45, what is (1) the percentage return and (2) the annual compound rate of return using time value of money? Round your answers to two decimal places.

Percentage return: _______%

The annual compound rate of return:_______ %

2. How many seven – letter code words can be formed using a standard 26 letter alphabet (12 points)

a.         if repetition is allowed?

b.         if repetition is not allowed?

c.         if the first letter has to be a C and the rest of the letters are different?

d.         if the first two letters have to be a vowel and the rest of the letters are different?

Bonds A and B are both seven-year bonds with annual coupon payments. Bond A has a higher coupon rate and higher yield. Given this information, is it possible to determine which of the two bonds has higher duration (D)? If yes, identify this bond and explain why it has higher duration. If not possible, explain why not.

Five people on the basement of a building get on an elevator that stops at seven floors. Assuming that each has an equal probability of going to any floor, find

(a) the probability that they all get off at different floors

(b) the probability that two people get off at the same floor and all others get off at different floors.

Two automobiles collide. One automobile of mass 1.13 x 10³ kg is initially traveling at 25.7m/s [E]. The other automobile of mass 1.25 x 10³ kg has an initial velocity of 13.8 m/s [W]. The vehicles become attached during the collision

            (a) Determine the magnitude and direction of the change in momentum for each automobile in question 7.

            (b) How are these two quantities related?

            (c) What is the total change in the momentum of the two automobile systems?

A sealed container of volume 7 m³ has two compartments with a barrier in between them. In one compartment, there is O2 at an initial pressure of 3 atm, initial temperature of 540 K, and volume 3 m³. In the other compartment, there is CO2 at an initial pressure of 5 atm, initial temperature of 430 K, and volume 4 m³. The barrier in the middle is punctured and the two gases mix together. What is the final pressure and temperature of the two gases and what is the change in entropy of the universe after the gases combine

Stephanie is going to contribute $300 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will contribute 50 percent of the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly rate of 0.9 percent, how much will she have in her retirement account 35 years from now?