1. Three players, A,B, and C, each flip their coins until one person has a different result from the others. The person having the different result wins.

(a) Using R, simulate this experiment 10000 times and give the resulting estimate of P(A wins).

I need A and C

Use a priority queue to simulate prioritized jobs

• Priority Queue class
  • Queue Class
  • Node Class (Node will have a 4 digit job number and a priority (A, B, etc) with A highest priority
• In the driver
  • Create a priority queue object
  • Add 3 jobs of 'B' priority
  • Add 4 jobs of 'D' priority
  • Add 2 jobs of highest priority
  • Print the queue

#C.

Write a program that accepts any number of homework scores ranging in value from 0 through 10. Prompt the user for a new score if they enter a value outside of the specified range. Prompt the user for a new value if they enter an alphabetic character. Store the values in an array. Calculate the average excluding the lowest and highest scores. Display the average as well as the highest and lowest scores that were discarded.

A CBS News/New York Times survey found that 97% of Americans believe that texting while driving should be outlawed (CBS News website, January 5, 2015).

a. For a sample of 10 Americans, what is the probability that at least 8 say that they believe texting while driving should be outlawed? Use the binomial distribution probability function to answer this question (to 4 decimals).

b. For a sample of 100 Americans, what is the probability that at least 95 say that they believe texting while driving should be outlawed? Use the normal approximation of the binomial distribution to answer this question (to 4 decimals). Use “Continuity correction factor” method. Use Table 1 in Appendix B.

c. As the number of trials in a binomial distribution application becomes large, what is the advantage of using the normal approximation of the binomial distribution to compute probabilities?

d. When the number of trials for a binominal distribution application becomes large, would developers of statistical software packages prefer to use the binomial distribution probability function shown in Section 5.5 or the normal approximation of the binomial distribution discussed in Section 6.3?

Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,500 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,500 and $14,600.

1. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
   
   
2. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?
   
   
3. What amount should you bid to maximize the probability that you get the property (in dollars)?
   
   
4. Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid $13,250. If your objective is to maximize the expected profit, what is your bid?

What is the expected profit for this bid (in dollars)?

In a mixture of gases, like air, the gas with the largest mole fraction will have the -

KNIGHTS ENGINES INC.

The government has recently invited submissions from the private sector for the supply of one thousand V-16Z (Class A) automobile engines. Although these particular engines only have eight cylinders, they can easily duplicate the speed and performance of a sixteen cylinder engine. Their compact size and durability make them ideal for military operations and it is for this reason that the military has decided to incorporate them into their new line of All Terrain Vehicles (ATVs). For reasons that cannot be exposed without jeopardizing national security, the engines must be delivered within 60 days.

Knight Engines Inc. has been involved in the manufacture of a wide variety of engines for nearly five years. Although Knight has managed to turn a healthy profit every year, sales for its V-16Z engines have been lagging somewhat. It is for this reason that Knight is quite excited by the government's request for V-16Z engines. Knight has dealt with the government before and their established reputation would certainly be a bonus in their favor if another company were to submit an equally low bid. There is, however, one problem: Although Knight does have the capacity to build one thousand V-16Z automobile engines, they do not have the pistons required to make the Class A engines. Their regular piston supplier only manufactures inferior Class C pistons, which would be unacceptable to the government. Since one thousand engines are to be produced, eight thousand Class A pistons are required. If the Class A pistons could be acquired within two weeks, the two-month government deadline could be met.

Knight made inquiries at several companies and only one showed any interest in supplying Knight with all the Class A pistons that it needs on such short notice. The Excalibur Engine Parts Company stated that it would be possible to process such a rush order but that it would do so only on two conditions: First, that the chassis of any engine constructed with their pistons clearly states that it is fitted with Excalibur brand pistons. Second, that a 5% mark-up be applied due to the extra costs of processing such an order on short notice.

Although the technical aspect of fitting these pistons into the engines presents no problems, the people in manufacturing are rather concerned about using a new type of piston from a company with which Knight has no previous experience. They stated that on the average, about 3 to 4% of the Class C pistons ordered in the past (from other suppliers) contained various structural flaws that rendered them unusable. There is no reason to believe that the Class A pistons should fare any differently. It is therefore essential that Excalibur provide some sort of guarantee in order to ensure that Knight does not have to pay for defective pistons. Even with such a guarantee, the inevitable delays for the delivery of a replacement could hinder Knight's ability to complete its engines before the government deadline. In order to cushion against such a problem, it might be advisable to order extra pistons. Ideally, Excalibur would agree to take back all unused pistons as part of a guarantee package.

You are Knight's Director of Purchasing and it is your responsibility to negotiate a contract with Excalibur for their Class A pistons, the Series 2.1 Intensaflux pistons. Since the price paid for the piston will raise the overall cost of the engine and therefore affect the bid submitted to the government, it is paramount that the lowest possible price be paid. In order to strike a good deal, you must pay careful attention to the following points:

1. You have never before purchased Class A pistons. Your knowledge of the market for other pistons (for instance, the Class C pistons sell for $250 each) suggests that they should sell for about $500 per piston. The absolute maximum that could be paid per piston and still enable the submission of a competitive bid would be $600 per piston.

2. There is rumor that Excalibur has been trying to get its foot in the door with respect to government contracts. Many of your colleagues find it somewhat unreasonable that Excalibur should have a free ride on Knight's coattails by having their company name mentioned on all the Knight engines fitted with Excalibur pistons, especially when you consider that they are charging a 5% “rush” fee. Perhaps Excalibur should deduct 5% from their price in return for this advertising service. Still, you do not want to press this issue too far because your company president has told you that it might be in the interests of Knight to develop a good relationship with Excalibur's management since Knight may one day be in a position to acquire this smaller company.
3. A competitor of Excalibur, Mordred Technologies Inc., has stated emphatically that it would in no way be able to fulfill such a rush order for a similar piston in 2 weeks’ time. However, they did state that if Knight was willing to wait 4 weeks for shipment, they would gladly supply all the pistons required for $470 per piston. Although a 4-week delivery date would certainly not allow enough time to meet the government deadline, Knight could use these pistons to upgrade some engines in stock and await another government or private contract.

Questions:

1. How would you prepare for this negotiation?
2. Which items (price, speed of delivery, guarantees, long-term relationship) do you consider the most important?
3. What is the highest price you would consider (your walk-away price)?

A pendulum is swinging in an elevator that is accelerating upward at a constant acceleration a. (a) Using the Lagrangian method, what is the equation of motion? Note be careful here, the velocity needs to be measured from an inertial reference frame. (b) What is the frequency of small oscillations?

You are an engineer in charge of designing a new generation of elevators for a prospective upgrade to the Empire State Building. Before the state legislature votes on funding for the project, they would like you to prepare a report on the benefits of upgrading the elevators. One of the numbers that they have requested is the time it will take the elevator to go from the ground floor to the 102nd floor observatory. They are unlikely to approve the project unless the new elevators make the trip much faster than the old elevators.

If state law mandates that elevators cannot accelerate more than 4.50 m/s24.50 m/s2 or travel faster than 15.3 m/s15.3 m/s, what is the minimum time in which an elevator can travel the 373373 m from the ground floor to the observatory floor?

Elevators generally break down at random times and for different reasons. Elevator maintenance contractors must have trained service personnel to provide routine and emergency service. Shan On Elevator has 200 service personnel to maintain 1,000 elevators.

a. Suppose that Shan On has received a contract to maintain an additional 1,000 elevators. Do you expect that Shan On will need to double service personnel? Why or why not? b. Does the example in (a) illustrate economies of scale or scope?

c. Escalators and elevators use quite different technology and parts. But many clients operate both escalators and elevators. Are there any economies of scope for a contractor to maintain both escalators and elevators?

Kindly use a graph to illustrte the answer wherever neccesary

on this case study can you identify the main problem and what is the objectives? thank you