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- A manufacturer of exercise equipment knows that 15% of their products aredefective. They also know that only 35% of their customers will actually use the equipment in the first year after it is purchased. If there is a one-year warranty on the equipment, what proportion of the customers will actually make a valid warranty claim?Even though you have no symptoms, your doctor withes to test you for a raredisease that only 1 in 10,000 people of your age contract. The test is 98%accurate, which means that, if you have the disease, 98% of the times the testwill come out positive and 2% negative. Also, if you do not have the disease, the test will come out negative 96% of the time and positive 4% of the time. You take the test and it comes out positive. What is the probability that you have the disease?An organization published an article stating that in any one-year period, approximately 7.5 percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, six of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country. 1. Enter your answer to two decimal places. p' = 2. Calculate ?x. (Round your answer to three decimal places.) 3. Find the p-value. (Round your answer to four decimal places.)
- Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 99 percent reliable, this means that the test will yield an accurate positive result in 99% of the cases where the disease is actually present. Gestational diabetes affects 9+1 percent of the population in our patient’s age group, and that our test has a false positive rate of 9+4 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2: If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes? What is the probability of having the disease given that you test positive? If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes? What is the…A group of medical professionals is considering theconstruction of a private clinic. If the medical de-mand is high (i.e., there is a favorable market for theclinic), the physicians could realize a net profit of$100,000. If the market is not favorable, they couldlose $40,000. Of course, they don’t have to proceedat all, in which case there is no cost. In the absenceof any market data, the best the physicians can guessis that there is a 50–50 chance the clinic will be suc-cessful. Construct a decision tree to help analyze thisproblem. What should the medical professionals do?Suppose insurance agency services customers who have both a homeowner’s policy and an automobile policy. For each type of policy, a deductible amount must be specified. For an automobile policy, the choices are TZS100 and TZS250, whereas for a homeowner’s policy, the choices are 0, TZS100, and TZS200. Suppose also that an individual is selected at random from the agency’s files. Let X = his deductible amount on the auto policy and Y = his deductible amount on the homeowner’s policy (a) What are the possible (X, Y) pairs? (b) Suppose the joint probability mass function is given by the insurance company in the accompanying joint probability in the following Table Table: Discrete Joint Probability Distribution for X and Y P(x,y) 0 100 200 X 100 0.2 0.10 0.2 250 0.05 0.15 0.3 What is p (100, 100) What is P (Y greater than 100)?
- A nutritionist believes that obesity is more prevalent among American adults than it was in the past. He discovers that in a study conducted in the year 1994, 380 of the 1630 randomly chosen adults were classified as obese. However, in a more recent study, he finds 726 out of 2350 randomly chosen adults were classified as obese. At α = 0.05, do these studies provide evidence to support the nutritionist's claim that the proportion of obese adults has significantly increased since 1994?Suppose that there are 4 deaths due to stomach can- cer among workers in a tire plant from 1/1/64 to 12/31/83, while 2.5 are expected based on U.S. mortality rates. Provide a 95% CI for the expected number of deaths from stomach cancer over 20 years among the tire workers. Is the number of cases of stomach cancer excessive?The University of Metropolis requires its students to pass an examination in college-level mathematics before they can graduate. The students are given three chances to pass the exam; 55% pass it on their first attempt, 64% of those that take it a second time pass it then, and 43% of those that take it a third time pass it then. (Assume that all students who do not pass the first or second time elect to take the test again.)What percentage of the students are not allowed to graduate because of their performance on the exam? (Round your answer to one decimal place.)
- In August 2011, Bank of Hawaii (BOH) stock cost $45 per share, yielded 4% per year in dividends, and had a risk index of 3.0 per share, while JPMorgan Chase (JPM) stock cost $40 per share, yielded 2.5% per year in dividends, and had a risk index of 2.0 per share.† You have up to $25,000 to invest in these stocks, and would like to earn at least $796 in dividends over the course of a year. (Assume the dividends to be unchanged for the year.) How many shares (to the nearest tenth of a unit) of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio?In the city of AZ, there are two supermarkets, X-Mart and Y-Mart. It is assumed that every shopper makes a purchase once a week at one of these supermarkets (not both).In a study, 100 samples of shoppers were taken over 10 weeks. From the study, it is known that if a shopper goes to X-Mart in one week, 85 people will continue to shop at X-Mart in the following week, and if a shopper goes to Y-Mart in one week, 70 people will continue to shop at Y-Mart in the following week.Create a transition probability table and matrix for this scenario, and then If in the first week Ivankov buys from X-Mart, what is the probability that Terry will buy from X-Mart in the third and fourth weeks?The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 38 who smoke. Step 1 of 2: Suppose a sample of 273 Americans over 38 is drawn. Of these people, 79 smoke. Using the data, estimate the proportion of Americans over 38 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places. Step 2 of 2: Suppose a sample of 273 Americans over 38 is drawn. Of these people, 79 smoke. Using the data, construct the 85% confidence interval for the population proportion of Americans over 38 who smoke. Round your answers to three decimal places. Lower end point, upper end point