Q­−2: [2+3+3 marks] Find integers and such that .Find the GCD and LCM for the numbers 2772 and 37800.Encrypt the message “I NEED HELP” by translating the letters into numbers, applying the encryption function ,and then translating the numbers back into letters. Q­−3: [4×2] Let and be the functions from to .Find .Is onto? Is g one-to-one? Explain you answer.Check whether exists. If it is so, define . Otherwise, provide a reason for not existence of .Check whether exists. If it is so, define . Otherwise, provide a reason for not existence of . Q­−4: [4+4 marks] Of 32 people who save paper or bottles (or both) for recycling, 30 save paper and 14 save bottles. Find the number of people whoStudents need to answer 8 out of 10 questions in biology exam.save bothsave only paper, andsave only bottles.Find the number of the ways a student can choose the 8 questions.In how many ways can a student choose 8 questions if the first three questions are mandatory?In how many ways can a student choose 8 questions if at least 4 of the first 5 questions must be answered? Q­−5: [2+3+3 marks] Consider an experiment of rolling two dice, and assume that each simple event in the sample space is as likely as any other find the probability that:A sum of 7 turns up;A sum of 7 or 11 turns up; A sum is greater than

Please use excel not minitab Instructions (please read and follow the instructions):Please solve the problems using excel as the tool. For each problem, (1) specify the business and statistical hypotheses, (2) include screen shots of the results from excel, stating your specific answers separately from the screen shots (3) draw appropriate conclusions to your statistical hypotheses based on the results, and, finally, (4) present the business conclusions in a short non-statistical summary.1.Your hospital is negotiating with medical insurance providers, who would like to reduce the amount they pay as reimbursement for hospital stays. For a particular procedure, they would like to reduce payment by $300 and have patients go home one day earlier. To see what effect this would have on hospital costs, a random sample of 50 patients who were recently admitted for this procedure was analyzed. Had they left one day earlier, the average hospital cost would have been $322.44 less, and the standard deviation was found to be $21.71. Construct a 95% confidence interval for the mean net savings for the hospital, per patient, for the larger population of recent patients.The Glen Valley Steel Company manufactures steel bars. If the production process is working properly, it turns out steel bars with lengths that are normally distributed with a mean of at least 2.8 feet, with a standard deviation of 0.20 foot (as determined by the engineering specifications on the production equipment involved). Longer steel bars can be used or altered, but shorter steel bars must be scrapped. You select a sample of 25 bars, and the mean length is 2.73 feet. Do you need to adjust the production equipment? (use a significance level of 0.05.(Source: LSKB-5)Meier and Frank is a chain of department stores located in the Northwest. The company has issued its own credit cards for a number of years. As a new employee in the finance department, imagine that you have been assigned to a major investigation of the firm’s credit policies designed to reduce bad debt losses. You are requested to investigate the relationship between marital status at the time the card is issued and the subsequent payment record of the individual.You randomly select 100 credit cards issued three years previously. Of the 70 individuals that were married at the time the cards were issued, 11 have defaulted on a payment. Of the 30 individuals who were single when the cards were issued, 7 have defaulted. Do these data present sufficient evidence to indicate that marital status affects credit-worthiness? Use Alpha = 0.05.(Source: Unknown – 326RL?)The National Restaurant Association is interested in determining if there is a relationship between the type of pizza pie which Americans prefer and the region of the country in which they live. The association randomly selects 285 Americans and records the category of pizza pie which best describes their preference and the region of the country in which they live. The results are as follows:Type of Pizza Region Pie Preferred North South East West Thin Crust 40 30 35 45 Thick Crust 17 15 21 22 Pan Pizza 15 15 15 15 -----------------------------------------------------------At α = .10, what can the Association conclude? (Source: Unknown)Fancy Fish, a fine dining upscale restaurant in Northridge, California and 2016 Open Table Diners’ Choice award winner, is enjoying its eighteenth season of providing delectable food, exceptional service, and beautiful outdoor dining experiences. “Saturday - Half-off Bottled Wine Night” has made Fancy Fish one of the San Fernando Valley’s favorite restaurants. Every Saturday night, guests can enjoy half-off every bottle of wine on the wine list while dining in the restaurant or on the terrace. The owner began offering “Saturday - Half-off Bottled Wine Night” in 2010 as an incentive for guests to dine at Fancy Fish when the economy was in a recession. Now that the economy is booming, the owner is considering whether the promotion should be continued, or even expanded. One concern is the effect that the promotion is having on the overall revenue generated from sales to the participants.A random sample of 28 checks was collected over the course of one month of Saturday nights. Fourteen checks were from customers participating in the half-off promotion, and the other 14 checks were from customers not participating. The total revenue from each check (less alcohol, tax, and tip) is presented below. Do these data present sufficient evidence that the checks of participants is significantly different from checks of non-participants? What is your recommendation to the owner regarding the status of the promotion?With Wine DiscountW/O Wine Discount354635443629362948292960366443472447134936535051224432366. A major distillery for alcoholic beverages is interested in gaining a large share of the market composed of people aged 18-23 (in those states where 18 is the legal drinking age). Beer and wine are the traditional favorites of this age group. However, Bill Schuessler, the firm’s marketing manager, and Carol Pringle, manager of research and development, feel that a new version of distilled apple cider will appeal to this younger market. While they are sure that the alcohol content should remain below 5 percent, they are not sure exactly what it should be. Therefore, five versions of the cider have been prepared and each version has been tasted by a random sample of 25 young consumers. Each consumer has evaluated the drink on a 100-point scale, with the higher scores representing a greater liking for the product. The results of the test appear below. What should Schuessler and Pringle conclude?Version1% 2% 3% 4% 5%16 40 81 89 5318 62 81 95 2072 11 35 10 9857 49 16 70 6730 40 83 94 9216 63 35 06 0896 77 20 20 5939 93 64 20 4931 62 76 38 0378 91 19 47 3203 93 33 30 4774 42 33 28 7209 06 09 90 9542 23 12 42 2516 15 08 02 0421 45 40 74 2021 58 57 80 5056 61 78 95 9745 65 66 99 2491 34 84 98 4991 22 21 20 3550 07 38 14 2165 39 05 22 5827 50 96 13 4437 16 94 85 17(Source: Unknown)7. Morning House is a mail-order firm which carries a wide range of rather expensive art objects for homes and offices. It operates by advertising a particular item either in selected magazines or in a direct-mail program. Suppose the sales response varies widely by item and the firm’s management has been unable to predict in advance which items will sell well and which will not. Consequently the firm frequently experiences either stock-outs or excessive inventories.For many of the products Morning House sells, it is possible to order a limited amount for inventory and to place a subsequent order for delivery within two weeks. Thus, if the firm could make a early prediction of the ultimate sales of a product, its inventory problems would be greatly reduced. Since it takes approximately six weeks to receive 90% of the response to a given campaign, an accurate prediction of total sales made as late as the end of the first week of receiving orders would be useful.The first week’s sales and total sales of the last 12 campaigns of the firm are shown below. Can the first week’s sales be used to predict total sales? First week’s TotalCampaign Sales Sales 1 32 1672 20 913 114 5604 66 3355 18 706 125 6507 83 4018 65 3209 94 47010 5 1511 39 21012 50 265 -------------------------------------------- (Source: Unknown)Questions?

To complete this problem set:Download the ( Module One Problem Set Template Zip File (the pdf of the zip file is attached) and import into Overleaf.Complete each portion of the template. Type your solutions into the document using LaTeX.Note: Be sure to show all steps for arriving at your solution. Just giving an answer may not receive the full score.Export your work as a PDF file and submit it to your instructor.