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)

a) Based on recent statistics, Green Way Airlines expects 4.2% of its customers will be “no shows”. If the airline sold 260 seats for a flight, how many people would the airline expect as “no-shows”? (Round to the nearest whole number)

b) If the airplane can hold 254 passengers, can all those who show up at the gate get on the plane? Explain

4. Volunteers from Habitat for Humanity are painting 16 interior walls in new homes that have been built. Each wall measures 14 feet by 6 2/3 feet. a) If a gallon of paint covers 400 square feet, how many gallons will be required to paint all the walls? (Round to next whole number) b) If each gallon costs $27.95, find the cost of the project.

5. In a recent year, wind machines in the United States generated 17.8 billion kilowatt-hours of electricity (enough to power more than 1.6 million households). The nation's total electricity production was 4450 billion kilowatt-hours. What percent of the total electrical energy production was generated by wind machines?

6. If a 5 1/4 inch line on a map represents a 9-mile road, how many miles would be represented by a 3 1/2 inch line?

7. At a fire sale, items are being sold at 3/4 off the marked price. What is the sale price of an item that has a marked price of $156?

8. Sixteen ounces of mouthwash costs $3.49 while a 33-ounce container of the same brand costs $6.99. Which is a better buy? Why?

9. The price of gasoline jumped from $3.24 per gallon to $4.05 per gallon in one year. What was the percent increase?

10. You buy 2.75 yards of material at $4.80 per yard and pay $0.87 sales tax. What is the total cost for your purchase?

11. Ruth orders clothes from a retail catalog. She orders two turtleneck tops for $35 each, two pairs of stretch pants for $45 each, one winter jacket for $130, and three leather belts for $25 each. The shipping and handling charge for the order is $15. What is the total charge for Ruth's order?

12. A recipe for a wedding punch calls for 12 quarts of champagne. If the champagne comes in bottles that are 4/5 of a quart, how many bottles of champagne would be needed?

13. One bank offers a 4-year car loan at an annual simple interest rate of 7% plus a loan application fee of $45. A second bank offers 4-year car loans at an annual simple interest rate of 8% but no loan application fee. If you need to borrow $5800 to purchase a car, which of the two bank loans has the lesser loan cost? (Assume you keep the car for all 4 years.)

14. In a recent survey of new car buyers, 20 of 63 men said they would prefer to buy a silver car while 16 of 49 women said they would prefer silver. a) Which group has a stronger preference for silver cars? b) Explain your answer

15. How many acres are contained in 1 square mile? (1 mile = 5280 ft.; 1 acre = 43,560 sq. ft.)

5.

(a) Write down the Bernoulli’s equation and the continuity equation.

(b) The entry and exit mouths of an uneven water pipe have areas of 0.2 m2 and 0.05 m2, respectively. If water enters the pipe at a speed of 5m/s find the speed of water exiting the pipe.

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be greater than 12.1 ounces. Find the probability if the sample is just 1 cup.

An 80 cm by 80 cm square loop of wire lies in the xy-plane and has a resistance of 0.2 Ω. It sits in a time-dependent uniform magnetic field of [0.6 sin (3π t)k] T. What is the largest value that the induced current takes on?

Random samples of size n = 60 were selected from a binomial population with p = 0.2. Use the normal distribution to approximate the following probabilities. (Round your answers to four decimal places.)

(a)    

P(p̂ ≤ 0.22) =

(b)    

P(0.18 ≤ p̂ ≤ 0.22) =