The director of publications for a university is in charge of deciding how many programs to print for football games. Based on the data, the director has estimated the following probability distribution for the random variable X= number of programs sold at the university football game:

X 25,000 40,000 55,000 70,000

P(X) 0.1 0.3 0.45 0.15

a)Compute the expected number of program sold at the university football game.

b)Compute the variance of program sold at the university football game.

c) Each program cost $1.25 to print and sells for $3.25. Any programs left unsold at the end of the game are discarded. The director has decided to print ether 55,000 or 70,000. Which of these two options maximizes the expected profit from program?

A horseshoe for horseshoe pitching should not weigh less than 2.625 pounds. In a sample of 28 horseshoes. the average weight is 2.48 pounds with a sample standard deviation of 0.3 pounds. We wish to test H0: mu equals 2.625 against HA: mu space less than space 2.625 at alpha space equals space 0.05. You may assume the distribution of weights is approximately normal.

a) Are the hypotheses being tested right-tailed, left-tailed, or two-tailed?

b) Determine the value of the test statistic from the given data. Show your work for partial credit.

c) Determine the critical value (or p-value) for this test.

d) What do you conclude about the average weight of the population of horseshoes?

1. Engine oil (cp = 2100 J/kg-°C) is to be heated from 20 °C to 60 °C at a rate of 0.3 kg/s in a 2-cmdiameter thin-walled copper tube by condensing steam outside at a temperature of 130 °C (hfg = 2174 kJ/kg).

a. For an overall heat transfer coefficient of 650 W/m2 -°C, determine the rate of heat transfer and the length of tube required to achieve it. Determine also the rate of steam condensation, in kgsteam/sec. (Ans: 25.2 kW; 7.0 m)

b. What would the tube length have to be if we wanted to heat the oil to 100 °C in the same 2-cm diameter tube and at the same flow rate? How about heating to 120 °C?

4. The US Navy has operated a 76 Hz ELF radio transmitter to communicate with submarines. Find the wavelength of the radio wave in km. The distance from New York to Los Angeles is 3,944 km. How does the wavelength compare with this distance? (5 pts)

5. To image individual atoms in crystals using electromagnetic waves, you typically want the wavelength of the wave to equal the atomic spacing between atoms; this spacing is about 0.3×10-9 m for many crystals. What would be the frequency of the EM wave needed to image atoms in the crystal? (4 pts)
Would you characterize the wave as (a) visible light, (b) ultra-violet light, (c) x-ray, or (d) gamma-ray? (1 pt)

A honey bee of mass 135 mg has accumulated a static charge of +1.6 pC. The bee is returning to her hive by following the path shown in the figure. Because Earth has a naturally occurring electric field near ground level of around 100 V/m

pointing vertically downward, the bee experiences an electric force as she flies.

What is the change in the bee’s electric potential energy, Δ?electric,

as she flies from point A (0 m,0.3 m) to point B (5.5 m,4.0 m)?

Δ?electric=

Compute the ratio of the bee’s change in electric potential energy to her change in gravitational potential energy, Δ?electric/Δ?grav.

Δ?electric/Δ?grav=

We want to study the zinc concentration from a river. We have a sample of measurements taken in 25 different locations in a river with sample mean x = 3 and population standard deviation σ = 0.3. The population is normally distributed.

1. Find the 95% and 99% confidence intervals for the mean zinc concentration in the river.

2. Is the following statement correct? “If we repeat the same experiment multiple times and each time calculate the two confidence intervals in question 1, then they cover x approximately 95% and 99% times respectively.” State your reason.

3. If we simply take x as the estimate for µ, how large a sample is required if we want to be 90% confident that the error will not exceed 0.05?

You are looking at buying a house with a $180,000 loan amount. You have 2 options for this loan: 1) 15 Year Loan, you can get a monthly interest rate of 0.3% monthly. A) What is your monthly payment? B) What is the total amount you would pay out of pocket over the life of the loan? C) How much interest have you paid?

2) 30 year Loan, you can get a monthly interest rate of 0.3125% monthly. A) What is your monthly payment? B) What is the total amount you would pay over the life of the loan? C) How much interest have you paid?

Please do on excel and show formula/calculations

5. Altria is reexamining the costs of capital it uses to decide on investments in its two
primary businessesó food and tobacco. The two divisions have about the same market
value.
Altria has an equity beta of 0.95 and a debt/equity ratio of 25%. The companyís debt is
priced to yield an expected return of 8%. The average equity beta of publicly traded Örms
in the tobacco business is 1.2, the average debt beta is 0.3, and the average debt/equity
ratio of such Örms is 20%. The average equity beta of publicly traded Örms in the food
business is 0.9, the average debt beta is close to zero, and the debt/equity ratio of such
Örms is 80%. The current interest rate is 7.1%.
Estimate the cost of capital for each of the two businesses

A certain firm in the beverage industry is faced with the following Cobb-Douglas production function of Q left parenthesis L comma K right parenthesis equals 4 L to the power of 0.3 end exponent space K to the power of 0.5 end exponent

a) What is A P subscript L and APK? [6 marks]

b) What is the level of M P subscript L space end subscript and M P subscript K when K = 40 and L = 40 [12 marks]

c) According to the Cobb- Douglas function , calculate the MRTS when K =35 and L = 25 [6 marks]

d) Increase capital with 75% and labour with 75% and see what will happened to output level.

(Black-Scholes)

Assume S = $22.00, σ = 0.30, r = 0.05 p.a. continuously compounded, the stock pays a 1.0% p.a. continuous dividend and the option expires in a month.

(a) What is the price of a $20 strike call? (Leave 2 d.p. for the answer)

(b) What is the delta? (Leave 3 sig. fig. for the answer)

(c) If the stock price changes to $22.10 immediately, what is the approximate change of the call price based on delta? (Leave 3 sig. fig. for the answer)

(d) What is the percentage change in the option for a 1% change in the stock? (Leave 3 sig. fig. for the answer)

(e) What is the volatility of the call option? (Leave 2 d.p. for the answer)

(f) If the Sharpe ratio of the stock is 0.3. What is the Sharpe ratio of the call?