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

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.)

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?

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.…