1 In a certain factory manufacturing razor blades, there is a small chance, for any blade to be defective. The blades are placed in 50 packets, each containing 10 blades. Using the Poisson distribution, calculate the approximate number of packets containing not more than 2 defective blades in a consignment of 10000 packets.
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- 8. The probability distribution of weekly sales of TV sets in a retail depot is given berow : 12 13 14 15 Demand (units) 10 11 0-05 0-10 0.25 0-40 0-15 0-05 Probability The depot earIS a profit of should be stocked ? 700 per set. If it is not sold, the loss is 300 per set. How many setsQuestion (c) Compute cumulative frequencies and cumulative relative frequencies.(d) What is the percentage of days when more than 6 books were stolen?The assets (in billions of dollars) of the four wealthiest people in a particular country are 46, 33, 21, 12. Assume that samples of size n = 2 are randomly selected with replacement from this population of four values. a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distributi- of the sample mean. In the table, values of the sample mean that are the same have been combined. Probability Probability x 46 39.5 33.5 33 29 (Type integers or fractions.) CITR X 27 22.5 21 16.5 12
- 2) The average number of operational losses a year at a particular plant is 18, so the number of losses in a year is distributed Poisson, with a mean 18. a. Using the probability distribution formula for the Poisson distribution, What is the probability that there will exactly 12 operational losses in the next year ? b. Using the table lookup method, what is the probability of having less than three operational losses in one month ? 3) Given the distribution parameter from the previous question: a. What is the average number of weeks between operational losses ( assume 52 weeks per year ) ? b. What is the probability that two operational losses will occur within two weeks of each other ?In an area along a highway, the number of telephone connection failures per call follows a Poisson distribution. For four calls, the number of connection failures is 2 0 3 1 A) Find the MLE of lambdaB) Get the MLE that the next two calls will complete without connection failures100 among 600 articles are defective if the maximum Aries probability 0.99 is 0.02. Find the sample size.
- Three randomly selected households are surveyed. The numbers of people in the households are 2 , 7 , and 12 . Assume that samples of size nequals 2 are randomly selected with replacement from the population of 2 , 7 , and 12 . Construct a probability distribution table that describes the sampling distribution of the proportion of even numbers when samples of sizes nequals 2 are randomly selected. Does the mean of the sample proportions equal the proportion of even numbers in the population? Do the sample proportions target the value of the population proportion? Does the sample proportion make a good estimator of the population proportion? Listed below are the nine possible samples. 2 ,2 2 ,7 2 ,12 7 ,2 7 ,7 7 ,12 12 ,2 12 ,7 12 ,12On average, there is one hurricane in the Bahamas every year. The cost torepair the damage of each hurricane in the Bahamas to a particular resort is 100. To stabilizefinances, the resort buys hurricane insurance, which will cover the cost of the repairs foreach hurricane after the second. Assume that the number of hurricanes in the Bahamas ina given year is Poisson distributed. 1. What is the expected cost of repairs in a given year to the resort (not including thecost of insurance)?2. What is the expected payout of the insurance company on the resort’s policy in agiven year?10) The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 9.3 tickets per day. Find the probability that exactly four tickets are written on a randomly selected day from this distribution.
- Suppose that 77% of the students at a small private university carry student loans. For a SRS of students at this university, let P(hat) be the sample proportion of the students who carry student loans. How large would a sample from this population need to be to ensure that the distribution of the sample proportion is normally distributed?15.9% of persons under the age of 65 have no health insurance coverage. Suppose that 4 persons are selected.A) Determine probability distribution for the number, X, who have no health insurance coverage. For X = 1, 2, 3, and 4.B) Determine and interpret the mean of X.19) The number of goals scored at State College soccer games follows a Poisson process with a goal scored approximately every 18 minutes (a soccer game consists of 2 45-minute halves). What is the mean number of goals scored during a game