1. A marksman hits a target 0.73 of the time. He fires 10 shots at the target. Find the probability that he make exactly 8 hits using the binomial distribution.

3. The campus bookstore asked a random set of freshmen (group 1) and seniors (group 2) as to how much they spent on textbooks in that term. The books store would like to test if the average spending of Freshmen is at least $5.0 more than that of seniors. Which of the following is the correct alternative hypothesis (H1)?

6. Scores on a standard test are normally distributed with a mean of 37.3 and a standard deviation of 8. Find the probability that the score is between 37 and 42.
7. Let X be a continuous random variable whose probability density function is:    f(x) = 1.5 x²   for -1 < x < 1 and 0 else where.

Find the probability that the random variable is between -1.6 and -0.7.

HOUR DEADLINE PLEASE HELP

The energy flux of solar radiation arriving at Earth orbit is 1353 W/m2. The diameter of the sun is 1.39x109 m and the diameter of the Earth is 1.29x107 The distance between the sun and Earth is 1.5x1011 m.

(a) What is the emissive power of the sun as calculated from the parameters given above?

(b) Approximating the sun’s surface as black, what is its temperature (as calculated from the parameters given above)?

(c) At what wavelength is the spectral emissive power of the sun a maximum?

(d) Assuming the Earth’s surface to be black and the sun to be the only source of energy for the earth, estimate the Earth’s surface temperature. Assume that the Earth absorbtivity to solar irradiation is 0.7. The actual average temperature of the Earth is currently ~288 K. Why do you think there are differences between your prediction and the actual average temperature (assume that the given value of absorbtivity is correct)?

A process for making small amounts of hydrogen by cracking ammonia is being considered, and residual uncracked ammonia is to be r removed from the resulting gas. Design a tray type absorption column to remove NH₃ from a gas stream using water as solvent. The gas stream (flow rate = 0.7 kg/s) consists of H₂ and N₂ (in the molar ratio 3: 1) and 3% NH₃ by volume. The ammonia will be removed by scrubbing the gas countercurrently with pure liquid water (flow rate = 6 kg/s) in a sieve-tray tower. The exiting gas stream should have 1% NH₃. Assume that only NH₃ can dissolve in water, and other gases (N₂+H₂) are inerts. Conditions at bottom of tower: Temperature, T = 303 K, and Pressure = 200 kPa.

Determine:

The number of stages (trays), tray spacing, and the diameter of the absorption column

#1 A mass measurement system behaves as a second-order system (consisting of a mass = 50g, a spring, and a viscous damping element). To determine the damping the ratio, the system was exposed to a step input and decaying oscillating amplitude of the system output was measured. Results of these measurements showed that the damping ratio = 0.7 and the ringing frequency f_d =389 Hz. Calculate the following and report results using 3 significant digits minimum:

The natural frequency, in Hz

The spring constant, in kN/m

Logarithmic decrement ln(x₁/x_n)

The period of oscillation when the system is exposed to a step input, in milliseconds

The dynamic error, ?, at 450 Hz in % (include the sign of the error)

The phase and time delay between input and output for sinusoidal inputs of 450 Hz in rad and milliseconds, respectively

Can we use this system to measure mass in outer space? How? Use a diagram to explain.

Do the following using R. You must also turn in a copy of your R code.

(10) What is the probability a beta (1, 8) random variable is less than 0.13?

(11) What is the probability a beta (3, 9) random variable is greater than .4?

(12) What is the probability a beta (18,4.4) random variable is between 0.6 and 0.7?

(13) At what value of x is the probability that a beta (4, 7) random varable is less than x equal to .71? That is, for what x is P r(beta(4, 7) random variable < x) = .71?

(14) At what value of x is the probability that a beta (12.2, 25.7) random variable is less than x equal to .2? That is, for what x is P r(beta(12.2, 25.7) random variable < x) = .2?

You are signed up for Comcast internet service. This service requires a physical device, a cable modem, to connect you to the provider's internet service. You have two options:

1. buy the cable modem on the internet, this will cost about $100

2. rent the cable modem from the provider, this will cost about $10/month.

Assume the relevant investment rate of return is 0.7% APR on your money (this is petty cash, and would just be sitting in your high-interest savings account at best). Assume the lifetime of the device is 6 years.

What is net benefit to you of buying the device as compared to renting it?

Hint: find the present value of all the estimated rent payments for the lifetime of the device. compare to the present value of buying it outright. the 'benefit' may be positive or negative, depending on whether you give up more present-wealth renting or buying.

5. In lab #2 we used LINEST (Excel function) to determine the slope and uncertainties of the slope. Imagine that you are performing the following measurements: X Y 1 2.2 2 3.1 3 4.5 4 6.3 5 7.5 6 8.3 7 9.7 8 10.5 9 11.2 10 12.5

5.a. Using LINEST, calculate the slope and uncertainty of the slope for given data. Hint: Set your y column as your dependent variable and x column as your independent variable.

5.b. Calculate the mean value x , the standard deviation V y ,and standard deviation of the mean σ y of your ‘measured’ quantity X over N trials (number of runs). Xi (units) 0 .65 0.68 0.62 0.7 0.67 0.63 0.61 0.6 0.66 0.64

PLEASE SHOW WORK

Although the injuries tend to be less severe, heading a soccer ball carries many of the same dangers as getting hit by a blocker or tackler in a football game. Indeed, heading is now forbidden in many youth leagues. In a very simple model, calculate the impulse given to the skull and its average acceleration when struck by a soccer ball. Assume that a headed soccer ball undergoes an elastic collision lasting 0.7 ms in which it reverses direction. Consider two different heading techniques: (i) where the head effectively recoils on its own, independent of the body (ii) the head and body recoil together. Do calculations for both youth players and for adults.

                                                Youth              Adult

Soccer ball mass (kg)             0.375               0.425

Speed of kicked ball (m/s)      20                    35

Mass of skull (kg)                   3                      5

Mass of entire body (kg)        30                    60

You are considering starting a company that manufactures motorcycles. You are planning on financing your firm 40% equity and 60% debt. You estimate that your upfront costs will be $5M, and that you will earn an EBIT of $1M per year for the next 12 years. Ian's Finest motorcycles make motorcycles similar to the ones that you wish to manufacture. They have a CAPM equity beta of 1.9 and a debt to equity ratio of 0.7. The tax rate for both firms is 35%, the riskless rate is 3%, and the expected return on the S&P500 is 15%. Your cost of debt is 6%.

A). What is the asset beta of Ian's Finest motorcycles?

B). What is your unlevered cost of equity?

C). What is your firm’s equity beta?

D). What is your firm’s weighted average cost of capital?

E). What is the NPV of your proposed motorcycle company using the WACC method?

You are considering starting a company that manufactures racing bicycles. You are planning on financing your firm 40% equity and 60% debt. You estimate that your upfront costs will be $5M, and that you will earn an EBIT of $1M per year for the next 12 years.

Lightning Bolt Bikes makes racing bicycles similar to the ones that you wish to manufacture. They have a CAPM equity beta of 1.9 and a debt to equity ratio of 0.7. The tax rate for both firms is 35%, the riskless rate is 3%, and the expected return on the S&P500 is 15%

cost of debt is 6%.

A.What is the asset beta of Lightning Bolt Bikes and your unlevered cost of equity?

B. What is your firm’s equity beta?

C. What is your firm's weighted average cost of capital?

D. Use WACC method to find NPV of your proposed bicycle company?