(31) A baseball teams plays 182 games in a season and we are tracking their record over three seasons. Assume the probability the team wins each game in Season 1, Season 2, and Season 3 is 0.45, 0.6, and 0.4, respectively. Let X be the total number of games the team wins over the three seasons. (a) Use Poisson approximations to binomial distributions to estimate P(X = 260). (b) Use normal approximations to binomial distributions to estimate P(X > 270).
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- Suppose we roll 3 fair dice and let X be the number of twos we roll.(a) Find the probability mass function of X.(b) Find the expected value of X.(c) Find the variance of X.(d) Find the probability-generating function of X.(e) Find the moment-generating function of XLet the probability of winning a bet in a roulette game is 1/38.Find the probability of winning at least 1 time in 38 games with the Binomial formula and the Poisson's approximation to the Binomial distribution.Suppose that the number of traffic accident claims received in a month is modeled by Poisson distribution with intensity λ = 4. Assume that each traffic accident claim takes values $150, $300 or $450 equally likely. Calculate the probability that the total traffic accident claim amounts to exactly $1500.
- Yhmeer is watching a shower of meteors (shooting stars). During the shower, he sees meteors at an average rate of 1.3 per minute. (a) State the conditions required for a Poisson distribution to be a suitable model for the number of meteors which Yhmeer sees during a randomly selected minute (b) Using Excel or otherwise, determine the probability that, during one minute, Yhmeer sees (i) exactly one meteor (ii) at least 4 meteorsThe level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 44 mg/mi. A company has 2525 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.050.05 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.) ?= ?The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
- Suppose a dresser drawer has blue shirts, yellow shirts, red shirts, and green shirts so that if a shirt is pulled from the drawer at random, each color has an equal chance of being drawn. P(Green) = P(Blue) = P(Red) = P(Yellow) = ¼. Complete parts (a) – (d) to create a probability distribution for the number of yellow shirts if two shirts are pulled from the drawer at random (replacing the shirt after each draw). a. List each possible outcome for the colors of the shirts if two shirts are drawn randomly from the drawer. The teacher said there should be total of 16 outcomes, not 9 or 10. In my original answer, I have 10 outcomes when there should be 16. c.Find the probability of each event (not the probability from each outcome) from part (b). For my first answer, I had the probability of each outcome, and I should have the probability of each event.A manufacturing company claims that the number of machine breakdowns follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the time (in hours0 between successive breakdowns. assuming that the manufacturing company's claim is true, find the probability that the time between successive breakdowns is at most five hours.Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…