6. The odds of a given ticket winning the Powerball lottery is p = 1/292,201,338. When thejackpot gets large, the number of tickets bought can grow quite large: in 2016, the number oftickets sold reached n = 371,000,000 one week when the jackpot had grown to over a billiondollars. The number of winners can be modeled as a Poisson random variable with parameter1 = np. With this many tickets sold, what is the probability that there are no winners? Onewinner? Two winners?

The mean value λ is computed as follows:

Answered: 6. The odds of a given ticket winning…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Millo.09.
q3 imagine a hypothetical future in which we have geolocation data on all people in a city and complete access to their medical records. For this example, the total number of hospital visits in the city in the past year was 104,000 and the city is 20,000 hectares in size. Assume that the individuals who go to the hospital are randomly distributed around the city (i.e., the Poisson distribution can be used for the questions below). (provide all values to the nearest 0.0001 and be cautious about rounding error) If we randomly choose an hectare in the city, what is the probability that more than three people in that region went to the hospital in the past year? If we randomly chose two hectares in the city, what is the probability that exactly five people went to the hospital in each of the two regions (i.e., ten total) in the past year?
Despite all efforts by the quality control department, the fabric made at benton corporation always contains a few defects. A certain type of fabric made at this corporation contains an average of 0.51 defects per 500 yards. Using the Poisson formula, find the probability that the number of defects in a given 500-yard piece of this fabric will be between two and four.P(between 2 and 4) =
Data from 14 cities were combined for a 20-year period, and the total 280 city-years included a total of 87 homicides. After finding the mean number of homicides per city-year, find the probability that a randomly selected city-year has the following numbers of homicides, then compare the actual results to those expected by using the Poisson probabilities: Homicides each city-year a. 0 b. 1 C. 2 d. 3 e. 4 Actual results 205 64 10 1 0 a. P(0) = (Round to four decimal places as needed.) b. P(1) = (Round to four decimal places as needed.) c. P(2) = (Round to four decimal places as needed.) d. P(3)= (Round to four decimal places as needed.) e. P(4)= (Round to four decimal places as needed.)
Astronomers treat the number of stars in a given volume of space as a Poisson random variable. The density in the Milky Way Galaxy in the vicinity of our solar system is 1 star per 16 cubic light years. (a) What is the probability of 3 or more stars in 16 cubic light years? Probability =i 0.080 . [Round your answer to three decimal places (e.g. 98.765).] (b) How many cubic light years of space must be studied so that the probability of 1 or more stars exceeds 0.94? cubic light years of space. [Round your answer to the nearest integer.]
Burn Open TABLE 8.6 bond proposal for school construction will be submitted to the voters at the next municipal election. A major portion of the money derived from this bond issue will be used to build schools in a rapidly developing section of the city, and the remain- der will be used to renovate and update school buildings in the rest of the city. To assess the viability of the bond proposal, a random sample of n = 50 residents in the developing section and n₂ 100 residents from the other parts of the city were asked whether they plan to yote for the proposal. The results are tabulated in Table 8.6. Sample Values for Opinion on Bond Proposal Developing Section Rest of the City 50 100 Sample Size Number Favoring Proposal 38 65 Proportion Favoring Proposal 76 65 1. Estimate the difference in the true proportions favoring the bond proposal with a 99% confidence interval. 2. If both samples were pooled into one sample of size n = 150, with 103 in favor of the proposal, provide a point…
A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?
Example 4.2:- As shown in the table below that gives the age distribution of companies. Find the following probabilities: 1-Ages (30-39). 2-Age=45. 3-Age>50. 4-Age<40. individuals starting new 30 - 39 40- 49 50-59 60 - 69 Age Frequency 20 - 29 11 25 14 3
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 15 7 7 13 13 20 13 12 5 10 26 22 13 7 11 3 The sample mean is x = 12.3%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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.…

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