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- If A={f,i,l,m,o,g,r,a,p,h,y}A={f,i,l,m,o,g,r,a,p,h,y} and U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}, find A′A′.The market research department at a manufacturing plant determines that 30% of the people who purchase the plant's product during any month will not purchase it the next month. On the other hand, 40% of the people who do no purchase the product during any month will purchase it the next month. In a population of 1000 people, 200 people purchased the product this month. How many will purchase the product the next month and in 2 months.The management of a company know that in the past, 38% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 17% of their sales were from people who are over 50 years old. A sample of 225 customers was taken to see if these market shares had changed. In the sample, 75 people were under 30 years old, 100 people were between 30 and 50 years old, and 50 people were over 50 years old. What is the expected counts under the null for people over 50 years old? (round to 2 decimals) The value of the test statistic χ2 is: (round to 4 decimals) The p-value is: (round to 4 decimals) The conclusion is:
- There are X-Mart and Y-Mart convenience stores. It is assumed that each customer purchases once a week at one of the two supermarkets (but not both). In a study, a sample of 100 buyers was taken for 10 weeks. From this research it is known that if buyers go to X-mart store one week, 85 people will still buy at X-mart store the following week and if buyers go to Y-mart store one week, 70 people will still buy at Y-mart store. mart the following week. 1. Make a table and matrix of transition probabilities. 2. If John purchases at X-mart in the first week, what is the probability that Bob purchases at X-store in the third and fourth weeks?Consider a screening system that analyzes the luggage that is being loadedto a plane. Each package first goes through a screening device. If it passes the test there, then it is loaded to the plane. If it does not, the package goes to a second screening device. The procedure is similar for the second device: if the luggage passes the test, it is loaded to the plane, if it fails, it issent to a third device. Packages that passes the test at third device are loladed to the plane, the ones that fail are taken paprt and not loaded to the plane.The screening devices i = 1; 2; 3 are not perfect. For each device, there are two risks:– With probability pi, each device erroneously passes a bag that is dangerous, given that previous devices have correctly rejected the bag.– With probability qi, each device erroneously fails a harmless bag that previous devices have also erroneously failed.Assume that pi; qi > 0 What is the probability that a dangerous package will be loaded to the aircraft?…2. A research Development department at Oda manufacturing company determines that 20% of people who purchase their products during any given month will not purchase the next month. On the other hand, 30% of the people who could not purchase during any given month will purchase in the next month. On a population of 1000 people 100 purchased their products this month. How many will purchase their product. 1. In the long run?
- a company manufactures a total of 8000 motorcycles a month in three plants A, B and C Of the 8000 motorcycles , plant A manufactures 4000, and plant B manufacturers 3000. At plant A, 85 out of 100 motorcycles are of standard quality or better. At plant B, 65 out of 100 motorcycles are of standard quality or better. At plant B, 65 out of 100 motorcycles are of standard quality or better and at plant C, 60 out of 100 motorcycles are of standard quality or better.The quality controller randomly selects a motorcycle: a) Caculate the probability that its qualtiy is sub-standard, b) If the motorcycle is of sub-standard quality calculate the probability that it has come from plant B.Suppose that 15% of a Canadian wholesaler’s food products are gluten-free. Furthermore, 70% of its products are peanut-free. Assume that the use of nuts and gluten-containing products are independent. 1. (a) What percentage of this wholesaler’s products contain at least one of the two allergens? (b) What percentage of this wholesaler’s products are allergen-free? 2. What percentage of this wholesaler’s products contain peanuts but no gluten?Exercise 3: In a garden center: 25% of the plants are less than a year old, 60% are 1 to 2 years old, 25% have yellow flowers, 60% have pink flowers, 15% have yellow flowers and less than a year old , 3% are more than 2 years old and have neither yellow nor pink flowers. 15% of those who are 1 to 2 years old have yellow flowers, 15% of those 1-2 years old have neither yellow nor pink flowers. It is assumed that the flowers cannot be both yellow and pink at the same time. We choose a plant at random in this garden center. What is the probability that it is less than a year old and has pink flowers? What is the probability that she has pink flowers, given that she is over 2 years old? What is the probability that it is over two years old and has yellow flowers?
- Most railroad cars are owned by individual railroad companies. When a car leaves its home railroad's trackage, it becomes part of a national pool of cars and can be used by other railroads. The rules governing the use of these pooled cars are designed to eventually return the car to the home trackage. A particular railroad found that each month 60% of its boxcars on the home trackage left to join the national pool and 79% of its boxcars in the national pool were returned to the home trackage. If these percentages remain valid for a long period of time, what percentage of its boxcars can this railroad expect to have on its home trackage in the long run?4. A graduate student in Health and Human Performance is interested in the effects of background noise on learning. He finds 18 undergraduate students who are willing to be part of the experiment. Well, the $100 Amazon gift card made it easy to find participants quickly. In any case, the students were randomly assigned to one of three treatments: 1) constant background noise; 2) random background noise; and 3) no background noise. The students were given material to study for one hour under these conditions. After that one hour, each student took a 20-point multiple-choice test. The scores for each student were as follows: constant noise: 16,17,14,15,16,13 random noise: 18,13,12,15,12,11 no noise: 20,19,18,16,15,17 a) What are the null and alternative hypotheses for this study? What statistical test should be used for this study? Justify your answer. b) Calculate your appropriate test statistic. Please show all of your work. c) Assume that the graduate set α to 0.05 during the…When looking at the data for graduate school admissions between men and women, it is shown that about 45% of men are admitted but only 38% of women. However, when the data is broken down by school it turns out that, within each school, the women are admitted at higher rates than the men. This could happen because I. The women apply in higher numbers to schools with lower acceptance rates. II. The women apply in higher numbers to schools with higher acceptance rates III. The men apply in higher numbers to schools with lower acceptance rates IV. The men apply in higher numbers to schools with higher acceptance rates
