A random sample of size n = 2 is chosen without replacement from the set{ 1 , 2 , 3 } . X = 0 if the first number is even, and X = 1 if the first number is odd. Y = 0 if the second number is even, and Y = 1 if the second number is odd.

a) List all of the samples.
(b) Find the joint distribution of X and Y.
(c) Are X and Y independent? Explain your answer.

1. XYZ Manufacturing Company buys 50 tons of coal per month. The price of 50 tons of coal can vary from month to month according to the table shown below:

How much should XYZ budget for coal in 2020? Your answer should be an integer.

2.

Replacement times for computer displays players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years.

If you want to provide a warranty so that only 2% of the computer displays will be replaced before the warranty expires, what is the time length of the warranty? Include 1 decimal place in your answer.

3. The amount of time a person waits for an elevator in a building is known to follow a uniform distribution between 0 and 60 seconds. What is the expected value of the wait time for an elevator? Your answer should be an integer. What is the probability that a person will wait between 20 and 35 seconds? Include 2 decimal laces in your answer.

4. The Hawaiian alphabet has twelve letters: five vowels (a, e, i, o, and u) and seven consonants (h, k, l, m, n, p, and w). For the purpose of this exercise we will define an n–letter “word” as an ordered collection of n of these twelve letters with repeats allowed. Obviously, most such “words” will be nonsense words.

a) How many possible four–letter Hawaiian “words” are there?

b) What is the probability a randomly selected four–letter “word” has no repeated letter?

c) What is the probability a randomly selected four–letter “word” contains three different consonants and one vowel?

d) What is the probability a randomly selected four–letter “word” starts with a consonant?

e) What is the probability a randomly selected four–letter “word” contains exactly one consonant?

Hello,

please solve it with Example. Thank you.

• apply the terminology of decision making to describe business problems
• compare and contrast deterministic and probabilistic models

Action Items

• Using the definitions found in Chapter 1 of Quantitative Analysis, the Internet, and your own personal experiences, make notes on and post one example of each of the following to the class Discussion Board topic "Deterministic and Probabilistic Models".
  • A deterministic model;
  • A probabilistic model; and
  • A situation in which you could use post optimality analysis (also known as sensitivity analysis).

Submission Instructions

Complete and submit this assignment per your professor's instructions.

Grading Criteria

Math test anxiety can be found throughout the general population. A study of 250 seniors at a local high school was conducted. The following table was produced from the data. Complete the missing parts.

i need step and method for the solution of the problem

Hypothesis testing is a statistical procedure for assessing claims about parameters or statistics? a. parameters b. statistics

QUESTION 2 A claim made about a parameter is called the _____ hypothesis. a. alternative b. null

QUESTION 3 The statement that you want to find statistical evidence for is the _____ hypothesis. a. alternative b. null

QUESTION 4 If statistical evidence is found against the null hypothesis, then we _____ the null hypothesis. a. fail to reject b. reject

QUESTION 5 Suppose the null hypothesis is H subscript 0 : space mu equals 100. Which sample result would be the best indicator that the null hypothesis is false? a. top enclose x space equals 105 b. top enclose x equals 97 c. top enclose x equals 120

QUESTION 6 A t-test is used to test hypotheses for the population mean mu. A random sample of 25 is selected for the analysis. How many degrees of freedom would be used for the test?

QUESTION 7 A t-test is used to test the null hypotheses H subscript 0 : mu equals 100. A random sample of 25 values gave a sample mean top enclose x = 110 and a sample standard deviation s = 20. What is the value of the t test statistic? a. -2.5 b. 2.5 c. 12.5 d. 0.08

QUESTION 8 A test of hypotheses is carried out at the alpha = 0.05 level. The P-value for the applied test is calculated to be 0.08. The decision is made to reject the null hypothesis. The correct decision is made in this case? True False

Most transshipment network modeling problems assume the costs are constant. For example, the costs of shipping a product from one city to another are assumed fixed. This can change over time if fuel costs change. If you knew the distribution of fuel costs, how could the distribution of fuel costs be incorporated into the transshipment problem? Discuss the benefits of employing this approach.

Major consulting firms such as Accenture, Ernst & Young Consulting, and Deloitte & Touche Consulting employ statistical analysis to assess the effectiveness of the systems they design for their customers. In this case, a consulting firm has developed an electronic billing system for a Stockton, CA, trucking company. The system sends invoices electronically to each customer’s computer and allows customers to easily check and correct errors. It is hoped the new billing system will substantially reduce the amount of time it takes customers to make payments. Typical payment times—measured from the date on an invoice to the date payment is received—using the trucking company’s old billing system had been 39 days or more. This exceeded the industry standard payment time of 30 days.

The new billing system does not automatically compute the payment time for each invoice because there is no continuing need for this information. The management consulting firm believes the new system will reduce the mean bill payment time by more than 50 percent. The mean payment time using the old billing system was approximately equal to, but no less than, 39 days. Therefore, if µ denotes the new mean payment time, the consulting firm believes that µ will be less than 19.5 days. Therefore, to assess the system’s effectiveness (whether µ < 19.5 days), the consulting firm selects a random sample of 65 invoices from the 7,823 invoices processed during the first three months of the new system’s operation. Whereas this is the first time the consulting company has installed an electronic billing system in a trucking company, the firm has installed electronic billing systems in other types of companies.

Analysis of results from these other companies show, although the population mean payment time varies from company to company, the population standard deviation of payment times is the same for different companies and equals 4.2 days. The payment times for the 65 sample invoices are manually determined and are given in the Excel^® spreadsheet named “The Payment Time Case”. If this sample can be used to establish that new billing system substantially reduces payment times, the consulting firm plans to market the system to other trucking firms.

• Assuming the standard deviation of the payment times for all payments is 4.2 days, construct a 95% confidence interval estimate to determine whether the new billing system was effective. State the interpretation of 95% confidence interval and state whether or not the billing system was effective.
• Using the 95% confidence interval, can we be 95% confident that µ ≤ 19.5 days?
• Using the 99% confidence interval, can we be 99% confident that µ ≤ 19.5 days?
• If the population mean payment time is 19.5 days, what is the probability of observing a sample mean payment time of 65 invoices less than or equal to 18.1077 days?

In this exercise we examine the effects of overbooking in the airline industry. Ontario Gateway Airlines' first class cabins have 10 seats in each plane. Ontario's overbooking policy is to sell up to 11 first class tickets, since cancellations and no-shows are always possible (and indeed are quite likely). For a given flight on Ontario Gateway, there were 11 first class tickets sold. Suppose that each of the 11 persons who purchased tickets has a 20% chance of not showing up for the flight, and that the events that different persons show up for the flight are independent. The money for tickets to the passengers who didn’t show up are returned.

(a) What is the probability that at most 5 of the 11 persons who purchased first class tickets show up for the flight?

(b) What is the probability that exactly 10 of the persons who purchased first class tickets show up for the flight?

(c) Suppose that there are 10 seats in first class available and that the cost of each first class ticket is $1,200. (This $1,200 contributes entirely to profit since the variable cost associated with a passenger on a flight is close to zero.) Suppose further that any overbooked seat costs the airline $3,000, which is the cost of the free ticket issued the passenger plus some potential cost in damaged customer relations. (First class passengers do not expect to be bumped!) Thus, for example, if 10 of the first class passengers show up for the flight, the airline's profit is $12,000. If 11 first class passengers show up, the profit is $9,000. What is the expected profit from first class passengers for this flight?

(d) Suppose that only 10 first class tickets were sold. What would be the expected profit from first class passengers for this flight?

(e) People often travel in groups of two or more. Does this affect the independence assumption about passenger behavior?

CASE STUDY CH.6 A spice manufacturer has a machine that fills bottles. The bottles are labeled 16 grams net weight so the company wants to have that much spice in each bottle. The company knows that just like any packaging process this packaging process is not perfect and that there will some variation in the amount filled. If the machine is set at exactly 16 grams and the normal distribution applies, then about half of the bottles will be underweight making the company vulnerable to bad publicity and potential lawsuits. To prevent underweight bottles, the manufacturer has set the mean a little higher than 16 grams. Based on their experience with the packaging machine, the company believes that the amount of spice in the bottle fits a normal distribution with a standard deviation of 0.2 grams. The company decides to set the machine to put an average 16.3 grams of spice in each bottle.

A businesswomen was interested in determining whether there is a significant difference in the average monthly cost per child for childcare outside the home between state supported facilities and privately owned facilities. Two independent random samples were selected yielding the following information:

1. Find a 90% confidence interval for the true difference in average monthly cost of the childcare.
2.    Based on the interval in a), can one conclude there is a significant difference in average cost of childcare between the state supported facilities and privately owned facilities? Justify your answer.

Each of the following pairs of null and alternative hypothesis has some error. Identify the error and explain how to fix it.

A 4 member relay team (including the order in which they will swim) is to be randomly selected from the 9 members of a men's swimming club.

a) How many different teams are possible?

b) Find the probability that the best swimmer is left off the randomly selected relay team.

c) Find the probability that the best swimmer is picked for the team, and asked to swim the fourth lap of the relay.

d) Find the probability that the top two swimmers in the club wind up swimming the third and fourth laps of the race, in either order;

i.e., the best could be either the third or fourth into the poo

The American Management Association wishes to have information on the mean income of middle managers in the retail industry. A random sample of 256 managers reveals a sample mean of $45,420. The standard deviation of this population is $2,050. The association would like answers to the following questions: a) Can we determine what the actual population mean is? b) What is a reasonable range (with 95% confidence) of values for the population mean? c)Explain in words to the Association what these results tell them.

Grades on a standardized test are known to have a mean of 940 for students in the United States. The test is administered to 436 randomly selected students in​ Florida; in this​ sample, the mean is 952.22 and the standard deviation ​(s​) is 101.52.

a) The​ 95% confidence interval for the average test score for Florida students is ​( 942.67​, 961.77​). ​(Round your responses to two decimal places.​)

b) Is there statistically significant evidence that Florida students perform differently than other students in the United​ States?

The​ 95% confidence interval for the average test score for Florida students does not include mu ​= 940​, so the null hypothesis that mu ​= 940 ​(that Florida students have the same average performance as other students in the United​ States) can be rejected at the​ 5% level.

c) Another 486 students are selected at random from Florida. They are given a​ 3-hour preparation course before the test is administered. Their average test score is 957.86 with a standard deviation of 89.30. The​ 95% confidence interval for the change in average test score associated with the prep course is ​( nothing​, nothing​). ​(Round your responses to two decimal places.​)