According to statistics, the distribution of ages for licensed drivers has a mean of 44.5 years and a standard deviation of 17.1 years. Assume the distribution of ages is normally distributed. (Give your answers correct to one decimal place.)

(a) What percentage of the drivers are between the ages of 17 and 22.
_______%

(b) What percentage of the drivers are younger than 25 years of age.
_____%

(c) What percentage of the drivers are older than 21 years of age.
______ %

(d) What percentage of the drivers are between the ages of 45 and 65.
_______%

(e) What percentage of the drivers are older than 75 years of age.
_______%

Bob and Carol Packer operate a successful outdoor wear store in Vermont called Northwoods Backpackers. They stock mostly cold-weather outdoor items such as hiking and backpacking clothes, gear, and accessories. They established an excellent reputation throughout New England for quality products and service. Eventually, Bob and Carol noticed that more and more of their sales were from customers who did not live in the immediate vicinity but were calling in orders on the telephone. As a result, the Packers decided to distribute a catalog and establish a phone-order service. The order department consisted of five operators working eight hours per day from 10:00 A.M. to 6:00 P.M., Monday through Friday. For a few years the mail-order service was only moderately successful; the Packers just about broke even on their investment. However, during the holiday season of the third year of the catalog order service, they were overwhelmed with phone orders. Although they made a substantial profit, they were concerned about the large number of lost sales they estimated they incurred. Based on information provided by the telephone company regarding call volume and complaints from customers, the Packers estimated they lost sales of approximately $100,000. Also they felt they had lost a substantial number of old and potentially new customers because of the poor service of the catalog order department.

Prior to the next holiday season, the Packers explored several alternatives for improving the catalog order service. The current system includes the five original operators with computer terminals who work eight-hour days, five days per week. The Packers have hired a consultant to study this system, and she reported that the time for an operator to take a customer order is exponentially distributed with a mean of 3.6 minutes. Calls are expected to arrive at the telephone center during the six-week holiday season according to a Poisson distribution with a mean rate of 175 calls per hour. When all operators are busy, callers are put on hold, listening to music until an operator can answer. Waiting calls are answered on a first-in, first-out basis. Based on her experience with other catalog telephone order operations and data from Northwoods Backpackers, the consultant has determined that if Northwoods Backpackers can reduce customer call waiting time to approximately one-half minute or less, the company will save $135,000 in lost sales during the coming holiday season.

Therefore, the Packers have adopted this level of call service as their goal. However, in addition to simply avoiding lost sales, the Packers believe it is important to reduce waiting time to maintain their reputation for good customer service. Thus, they would like about 70 percent of their callers to receive immediate service.

The Packers can maintain the same number of workstations/computer terminals they currently have and increase their service to sixteen hours per day with two operator shifts running from 8:00 A.M. to midnight. The Packers believe when customers become aware of their extended hours the calls will spread out uniformly, resulting in a new call average arrival rate of 87.5 calls per hour (still Poisson distributed). This schedule change would cost Northwoods Backpackers approximately $11,500 for the six-week holiday season.

Another alternative for reducing customer waiting times is to offer weekend service. However, the Packers believe that if they do offer weekend service, it must coincide with whatever service they offer during the week. In other words, if they have phone order service eight hours per day during the week, they must have the same service during the weekend; the same is true with sixteen-hours-per-day service. They feel that if weekend hours differ from weekday hours it will confuse customers. If eight-hour service is offered seven days per week, the new call arrival rate will be reduced to 125 calls per hour at a cost of $3,600. If Northwoods offers sixteen-hour service, the mean call arrival rate will be reduced to 62.5 calls hour, at a cost of $7,300.

Still another possibility is to add more operator stations. Each station includes a desk, an operator, a phone, and a computer terminal. An additional station that is in operation five days per week, eight hours per day, will cost $2,900 for the holiday season. For a sixteen-hour day the cost per new station is $4,700. For seven-day service the cost of an additional station for eight-hour per-day service is $3,800; for sixteen-hour-per-day service the cost is $6,300.

The facility Northwoods Backpackers uses to house its operators can accommodate a maximum of ten stations. Additional operators in excess of ten would require the Packers to lease, remodel, and wire a new facility, which is a capital expenditure they do not want to undertake this holiday season. Alternatively, the Packers do not want to reduce their current number of operator stations.

Determine what order service configuration the Packers should use to achieve their goals, and explain your recommendation.

Suppose a multiple regression model is given by modifying above y with caretequals0.21x 1minus9.52x 2minus28.56. What would an interpretation of the coefficient of x 1 be? Fill in the blank below. An interpretation of the coefficient of x 1 would be, "if x 1 decreases by ?? unit, then the response variable will decrease by nothing units, on average, while holding x 2 constant."

By how many units?

Ex. 2.40 European roulette.

The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their colour, they double their money. If it lands on another colour, they lose their money.

(a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings?

(b) Suppose you bet $1 in three different rounds. What is the expected value and standard deviation of your total winnings?

(c) How do your answers to parts (a) and (b) compare? What does this say about the riskiness of the two games?

Ex. 2.34 Ace of clubs wins.

Consider the following card game with a well-shuffled deck of cards. If you draw a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $20 for the ace of clubs.

(a) Create a probability model for the amount you win at this game. Also, find the expected winnings for a single game and the standard deviation of the winnings.

(b) What is the maximum amount you would be willing to pay to play this game? Explain your reasoning.

Plz use both pure NE and MIXED strategy (with Probability)

Consider a firm with two agents – 1 and 2. Both agents have to choose between two options: Client Focus or Cost Focus. If both choose Client the payoffs to 1 are 20 and 10 to agent 2. If both agents choose to play Cost the payoffs are 15 to agent 1 and 25 to agent 2, respectively. Finally, if any other combination of actions is chosen the payoffs to each agent are 0.

a. Assume that the agent choose their actions simultaneously. Draw the normal form of the game and derive all of the Nash equilibria.

b. Now assume that the game is played sequentially: Agent 1 makes her choice of action first, this is observed by Agent 2, who then makes his choice. Draw the extensive form of the game and find the subgame perfect equilibria. Briefly interpret this game in the context of: (i) leadership and corporate culture; and (ii) the Basic Value Maximisation Principle.

newspaper publisher is considering launching a new "national" newspaper in Anytown. It is believed that the newspaper would have to capture over 12% of the market in order to be financially viable. During the planning stages of this newspaper, a market survey was conducted of a sample of 400 readers. After providing a brief description of the proposed newspaper, one question asked if the survey participant would subscribe to the newspaper if the cost did not exceed $20 per month. Suppose that 58 participants said they would subscribe.

a. Can the publisher conclude that the proposed newspaper will be financially viable? Perform the appropriate test at a 1% level of significance.

b. Suppose the actual value of the overall proportion of readers who would subscribe to this newspaper is 0.13. Was the decision made in part (a) correct? If not, what type of error was made?

c. State the meaning of a Type I and Type II error in the context of this scenario. And what would be the repercussions of making these errors to the publisher?

An insurance company wants to monitor the quality of its procedures for handling loss claims from its auto insurance policyholders. Each month the company selects an SRS from all auto insurance claims filed that month to examine them for accuracy and promptness.

What kind of study was this?

A) Matched pairs experiment.   

B)Double blind experiment.

C) Observational Study.

D) Randomized comparative experiment.

*Please Explain*

A sample of 11 circuits from a large normal population has a mean resistance of 2.20 ohms. We know from past testing that the population standard deviation is 0.35 ohms.

1. Determine a 95% confidence interval for the true mean resistance of the population.

2. In part 1 above, do you need any assumptions, if yes what, if no why.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. A simple random sample of 25 filtered 100 mm cigarettes is​ obtained, and the tar content of each cigarette is measured. The sample has a mean of 20.2 mg and a standard deviation of 3.81 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes.

What are the​ hypotheses?

A. H0​: μ>21.1 mg

H1​: μ<21.1 mg

B.H0​: μ=21.1 mg

H1​: μ<21.1 mg

C.H0​: μ<21.1 mg

   H1​: μ ≥ 21.1 mg

D. H0​: μ =21.1 mg

H1​: μ ≥ 21.1mg

Identify the test statistic.

t = _________

Identify the​ P-value.

The​ P-value is ___________

State the final conclusion that addresses the original claim. Choose the correct answer below.

A. Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

B. Reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

C. Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

D.Fail to reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

What do the results​ suggest, if​ anything, about the effectiveness of the​ filters?

A.The results suggest that the filters are effective.

B.The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes.

C.The results do not suggest that the filters are effective.

D.The results suggest that the filters increase the tar content.

E.The results are inconclusive because the sample size is less than 30.

015824 A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 89 sample problems. The new algorithm completes the sample problems with a mean time of 17.64 hours. The current algorithm completes the sample problems with a mean time of 17.75 hours. Assume the population standard deviation for the new algorithm is 4.561 hours, while the current algorithm has a population standard deviation of 4.210 hours. Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let μ1 be the true mean completion time for the new algorithm and μ2 be the true mean completion time for the current algorithm. Step 1 of 5: State the null and alternative hypotheses for the test.

Compare the coding techniques used in quantitative versus qualitative research

Please conduct an independent-sample t-test, α = .05.  

Two persons are arguing about the size of different breeds of dogs. One believes that German Shepherds are larger than Huskies, while the other person believes the opposite is true. So they conducted a study to see which one of them is correct by randomly sampling and weighting 10 dogs of each breed they saw on a Sunday afternoon in their community. This is an independent-sample case. The data are as follows:

German Shepherds: 55, 72, 61, 43, 59, 70, 67, 49, 55, 63

Huskies: 48, 77, 46, 51, 60, 44, 53, 61, 52, 41

Sky Kitchens is the second largest airline caterer in the United States, providing nearly all the meals for passengers of three major airlines and several smaller commuter airlines. As part of a total quality management (TQM) program, its largest airline client, Continental Airlines, has recently met with representatives of Sky Kitchens to discuss a customer satisfaction program that it is planning to implement. Continental plans to interview a sample of its customers four times a year. In the survey, it intends to ask customers to rate the quality of meals provided on a 1–10 scale, where 1 means poor and 10 means excellent. It has just completed a benchmark study of 1,000 customers. In that study, meals received an average rating of 8.7 on the 10-point scale, with a standard deviation of 1.65. Continental has indicated that it wants Sky Kitchens to guarantee a level of satisfaction of 8.5 in the first quarterly survey, to be conducted in three months. For its quarterly surveys, Continental plans to use a sample size of 500. In the new contract with Sky Kitchens, Continental wants to include a clause that will penalize Sky Kitchens $50,000 for each one-tenth of a point it falls below an average of 8.5 on the next survey’s satisfaction scale.

1. What is the 99.74% confidence interval (CI) for the true satisfaction level based on the benchmark survey?

2. What is the 99% confidence interval (CI) for the true satisfaction level based on the benchmark survey?

3. What is the 95.44% CI for the true satisfaction level based on the benchmark survey?

4. What is the 95% CI for the true satisfaction level based on the benchmark survey?

5. As Sky Kitchens, what do you think of Continental’s requirement for a level of satisfaction of 8.5 in the first quarter survey?

6. Assume that the upcoming 1st -quarter satisfaction survey shows anaverage rating of 8.4 on satisfaction with meals. Assume that the population standard deviation is1.65. Compute the 99% CI for the true satisfaction level based on the 1st-quarter survey. As Sky Kitchens, what is the best way to present and interpret the resulting CI?

7. If you were negotiating for Sky Kitchens, how would you respond to Continental regarding the penalty clause? Is there a better or more reasonable way to revise it

Suppose that a deck of 52 cards contains 26 red cards and 26 black cards. Say we use the 52 cards to randomly distribute 13 cards each among two players (2 players receive 13 card each).

a. How many ways are there to pass out 13 cards to each of the two players?

b. What is the probability that player 1 will receive 13 cards of one color and player 2 receive 13 cards of the other color?

The Sorry State Lottery requires you to select five different numbers from 0 through 63. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.)

What is the probability of being a Big Winner?

What is the probability of being a Small-Fry Winner?

What is the probability that you are either a Big Winner or a Small-Fry Winner?