1. A beverage manufacturing company uses a pair of redundant pumps to transfer flavored syrups to the bottling line. Each pump has a λ of 0.055 failures per year and ß of 0.05. What is the probability that both pumps will fail during a 45 day production run? a. 0.00004 b. 0.00034 c. 0.00038 d. 0.12
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- A school board has a plan to increase participation in the PTA. Currently only about 27 parents attend meetings. Suppose the school board plan results in logistic growth of attendance. The school board believes their plan can eventually lead to an attendance level of 81 parents. In the absence of limiting factors, the school board believes its plan can increase participation by 10% each month. Let m denote the number of months since the participation plan was put in place, and let P be the number of parents attending PTA meetings. (a) What is the carrying capacity K for a logistic model of P versus m? K = (b) Find the constant b for a logistic model. b = (c) Find ther value for a logistic model. Round your answer to three decimal places. r = (d) Find a logistic model for P versus m. P =Textbook prices have a seasonal structure on Ebay. At the end of a term, the supply of used books outstrips demand, and the price is lower. Near the start of a term, many students are looking for books, and the price is higher. Suppose we can classify sales for a particular chemistry textbook into these two time periods and an "other" time period in the proportions shown below. We have also listed the average price the textbook sells for in each of these three time periods Start of Term End of Term Other Sales Proportion Average Price 0.43 0.31 0.26 97.97 49.93 73.83 For example, about 45% of Ebay auctions for this chemistry textbook occur at the start of the term and the books sell for an average of $82.52 during this time. Using the information above, compute the average price of the textbook over all seasons. (Do not put a dollar sign in your answer). Round your answer to two decimals. Average Price over all seasons = $C K 1. EXERCISE 1 A certain type of storage battery lasts, on average, 3.0 years with a variance of 0.25 year. O If the battery lives are normally distributed, find the probability that a given battery will last less than 2.3 years. 7. 8. 10 11 12 Solution: 14 15 16 17 18 19 20 21 22
- Part 1 only solve asap pleasePi- P2 Z. = %3D SE Suppose a drug company is developing a vaccine, designed to protect against a particular virus. The company states that the vaccine will be equally effective for men and women. In its initial stage, a researcher selects a random sample of 200 men and 100 women independently. At the end of the study, 15 of the men and 10 of the women showed symptoms of the virus after taking the vaccine. Is there enough evidence to conclude that there is a significant difference in the proportions of men and women who show symptoms of the virus after taking the vaccine? (a) State the appropriate hypotheses to answer this question. (b) Compute the test-statistic. (c) (i) Calculate the p-value. (ii) Interpret the p-value you have found. (d) State your conclusion in context of the situation. Page 1 135In a random experiment if a coin is tossed three times or three coins are tossed one time, if random variable X is the number of appearances of Tails, the value of E(X), will be; Select one: O a. None O b. 3.5 O c. 2.5 O d. 1.5
- Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?KOW 1 2 3 4 5 6 Decade Count 1851 1860 1861 1870 1871 1880 1881-1890 1891 - 1900 1901-1910 NO 6 1 7 5 00 8 4 1911-1920 8 1921-1930 5 LO 9 1931 1940 00 8 10 1941 - 1950 10 11 1951-1960 12 1961-1970 13 1971-1980 14 1981 1990. 4 15 1991-2000 16 2001 - 2010 9 17 2011-2020 саоттоа со 6 6 18 19 20 21 22 61° L var3 var4Random collections of nine different solutions of a calcium compound were given to two laboratories, A and B. Each laboratory measured the calcium content (in mmol per liter) and reported the results. The data are paired by calcium compound. Compound Lab A (x) Lab B (y) 1 2 3 4 7 9. 9.36 14.80 8.79 11.33 10.56 15.61 13.70 12.03 11.56 9.14 14.74 8.67 11.51 10.63 15.59 13.74 12.22 11.56 (a) Rank-order the data using 1 for the lowest calcium reading. Make a table of ranks to be used in a Spearman rank correlation test. Compound Lab A (x) Lab B (y) d = x – y d2 1 3 4 7 8 Ed? Compute the sample test statistic. (Round your answer to three decimal places.) II
- A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 15 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 15 volunteers were given placebo tablets. For each individual, the length of time taken to recover from the cold is recorded. At the end of the experiment the following data are obtained. Days to recover from a cold Treated with multivitamin 4.9. 3.9, 4.9. 7.3, 3.7, 5.7, 4.3, 6.1, 4.9, 5.4, 7.7, 7.3, 4.6, 4.3, 4.6 Treated with placebo 5.1, 5.3, 5.3, 1.6, 1.6, 4.8, 4.4, 3.3, 3.7, 5.2, 5.5, 5.8, 6.5, 1.5, 5.4 Send data to calculator Send data to Excel It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally…2. This question is about logistic regression. The outcome variable is success (1=success, 0=failure), and we have two groups of observations: group A and group B. a. Assume that on average, the odds of success is x for group A members. What is the average probability of success (p) for group A? Please write down p as a function of x. Given an x, is there a unique p? b. Assume that on average, the odds ratio for success of group A over group B is 2. The average probability of success for group A is pA and that the average probability of success for group B is pg. Is the set of Paand pg unique? c. The logistic regression of success ~ group (link=logit) returns a coefficient estimate of -1.3863 for the dummy variable group (1=group A, 0=group B). Interpret this coefficient estimate.An engineer designs a circuit, seen below. In this system, if the first component fails, the functionality moves immediately to the second component and so on. The system only fails when the fifth component fails. Each component has a lifetime that is exponentially distributed with λ = 0.01 and components fail independently of one another. Define A, to be the length of time component i lasts. Let Y = the time at which the new system fails. Given 2 لنا 5 A-Exponential (0.01) Y=A1+A2+A3+A4+A5 1. Find the probability that this new system will last fewer than 50 hours.