3. Consider Binomial(10, 0.3) distribution. Do the following tasks:

(b) Write down the mean and standard deviation of each distribution.

(c) Find the lower tail probability of 4.

(d) What is the probability that the value of the random variable is 2?

(e) What is the probability that the value of the random variable is greater than 2 and less than or equal to 4?

Let a firm’s production function be given by K^0.7 L^0.3.
(i) Sketch (without specific numbers) the shape of the long run average and long-run marginal cost curves of the firm; explain the key features of the sketch.
(ii) in the same graph, please also sketch the firm’s short run average and marginal cost curves (when the amount of capital is fixed). Comment on the relationship between the long- and the short-run curves depicted in your graph.

Sodium nitroprusside is ordered at 0.3 mcg/kg/min for a 220-lb patient. A vial containing 50 mg of sodium nitroprusside in 2 mL is diluted to 250 mL with NSI and ordered to run at 14 mL/h. Is this run rate correct? If not, what should be the correct infusion rate? The correct answer is no, and 9 mL/h. Please show how this problem is solved.

Consider a binomial experiment with n=13 and p=0.3

a. Compute f(0) (to 4 decimals).

b. Compute f(8) (to 4 decimals).

c. Compute P(x<=2) (to 4 decimals).

d. Compute P(x>=4) (to 4 decimals).

e. Compute E(x) (to 1 decimal).

f. Compute Var(x) and ó.

1. You are located downwind from two oil-burning power plants. One is located 0.3 km NE of your location and burns 1400 kg of 0.5% sulfur oil per hour. Its effective height is 60 m. The second plant is located 0.5 km NNW of you and burns 1600 kg/hr of fuel oil containing 0.75% sulfur. The effective height is 40 m. The wind is blowing from NNE at 3.3 m/s (measured at the standard height of 10 m). For a class B stability condition, what is the SO₂ concentration at your location at ground level?

Find the mean of this probability distribution. Round your answer to one decimal place.

2

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

3

2.36 Is it worth it?: Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs. Round answers to 2 decimal places.


a) Andy's expected profit per game is: $


b) Would you recommend this game to Andy as a good way to make money? Explain.

• Yes, Andy could be lucky and might earn money in the long-run playing this game
• No, we expect Andy to lose money each time he plays this game

4

2.38 Baggage fees: An airline charges the following baggage fees: $25 for the first bag and an extra $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have only one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags.


a) The average baggage-related revenue per passenger is: $ (please round to the nearest cent)
b) The standard deviation of baggage-related revenue is: $ (please round to the nearest cent)
c) About how much revenue should the airline expect for a flight of 120 passengers? $ (please round to the nearest dollar)

5

For a group of four 70-year old men, the probability distribution for the number xx who live through the next year is as given in the table below.

Verify that the table is indeed a probability distribution. Then find the mean of the distribution.
mean =
Report answer accurate to 1 decimal place.

6

Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and standard deviation of XX.

μμ =
σ2σ2 =
σσ =


What is the expected value of XX?

7

A bag contains 4 gold marbles, 9 silver marbles, and 24 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $3. If it costs $1 to play, what is your expected profit or loss if you play this game?

$

8

The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $3. There is 1 winning ticket out of the 180 tickets sold. The winner gets a prize worth $76. Round your answers to the nearest cent.

What is the expected value (to you) of one raffle ticket? $

I need help with this

thanks

1. Steam undergoes a state change from 450°C and 3.5 MPa to 150°C and 0.3 MPa.

Determine ΔH and ΔS using the following:

a. Steam table data

b. Ideal gas assumptions (be sure to use the ideal gas heat capacity for water).

(ANS: 0.0717 kJ/kg-K; -576.8 kJ/kg; 0.143 kJ/kg-K; -555.71 kJ/kg)

In 1815, The British Government issued a consol. If we assume the consol promised to pay $25 per year in perpetuity. What would the consol be worth if the discount rate is 5%?

Two stocks can be combined to form a riskless portfolio if the correlation of -1.0. Risk is not reduced at all if the two stocks have correlation of +1.0. In general, stocks have correlation less than 1.0, so the risk is lowered but not completely eliminated.

True

False

What is the beta for a market portfolio such as S&P 500 index portfolio?

Portfolio provides average return but much lower risk. The key is the negative correlations among individual stocks. As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.

If a stock’s expected rate of return is 12% and the required rate of return is 15%, the stock is believed to be ______

Which of the following statements about Security Market Line (SML) equation “r_i = r_RF + (r_M – r_RF)b_i = r_RF + (RP_M)b_i” is NOT true?

Particle Position and Time The position of a particle moving along the x axis depends on the time according to the equation x = ct² - bt³, where x is in meters and t in seconds.

(a) What dimension and units must c have?

s²/ms/m²     m/s²m²/s

What dimension and units must b have?

m³/ss/m³     s³/mm/s³

For the following, let the numerical values of c and b be 3.3 and 1.0 respectively.

(b) At what time does the particle reach its maximum positive x position?
s

(c) What distance does the particle cover in the first 4.0 s?
m

(d) What is its displacement from t = 0 to t = 4.0 s?
m

(e) What is its velocity at t = 1.0?
  m/s
What is its velocity at t = 2.0?
m/s
What is its velocity at t = 3.0?
  m/s
What is its velocity at t = 4.0 s?
m/s

(f) What is its acceleration at t = 1.0 s?
  m/s²
What is its acceleration at t = 2.0 s?
m/s²
What is its acceleration at t = 3.0 s?
  m/s²
What is its acceleration at t = 4.0 s?
m/s²

Suppose a batch of metal shafts produced in a manufacturing company have a variance of 6.25 and a mean diameter of 206 inches.

If 90 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.3 inches? Round your answer to four decimal places.