The number of requests for assistance received by a towing service is a Poisson process with rate a = 4 per hour. (a) Compute the probability that exactly eleven requests are received during a particular 5-hour period. (Round your answer to three decimal places.)
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- Consider a data set containing the following values: 92 84 85 93 95 89 86 91 The mean of the preceding values is 89.375. The deviations from the mean have been calculated as follows: 2.625 –5.375 –4.375 3.625 5.625 –0.375 –3.375 1.625 If this is sample data, the sample variance is and the sample standard deviation is . If this is population data, the population variance is and the population standard deviation is . Suppose the largest value of 95 in the data was misrecorded as 93. If you were to recalculate the variance and standard deviation with the 93 instead of the 95, your new values for the variance and standard deviation would be .Recall that 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. Now 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 = 215 numerical entries from the file and r = 50 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.(i) Test the claim that p is less than 0.301. Use ? = 0.10. (a) What is the level of significance?State the null and alternate hypotheses. H0: p = 0.301; H1: p < 0.301H0: p < 0.301; H1: p = 0.301 H0: p = 0.301; H1: p > 0.301H0: p = 0.301; H1: p ≠ 0.301 (b) What sampling…Marty's Barber Shop has one barber. Customers have an arrival rate of 2.3 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places. P0 = fill in the blank 1 What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places. P1 = fill in the blank 2 What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places. P2 = fill in the blank 3 What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places. P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer…
- A1The number of hits to a website follows a Poisson process. Hits occur at the rate of 1.1 per minute between 7:00 P.M. and 10:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 7:41 P.M. and 7:48 P.M. Interpret each result. (a) exactly four (b) fewer than four (c) at least fourGiven an arrival process with λ = 5.0, what is the probability that an arrival occurs after t = 7 time units?
- Recall that 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. Now 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 = 221 numerical entries from the file and r = 50 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. (i) Test the claim that p is less than 0.301. Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ho: P = 0.301; H₁: p = 0.301 Ho: P 0.301 Ho: P = 0.301; H₁: p 5 and nq > 5. O The Student's t, since np 5 and nq > 5. What is the value of the…Recall that 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. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 87 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. 1) Test the claim that p is more than 0.301. Use α = 0.10. 2) What is the value of the sample test statistic? (Round your answer to two decimal places.) 3) Find the P-value of the test statistic. (Round your answer to four decimal places.) 4) If p is in fact larger than 0.301, it would seem there are too many numbers in…The number of hits to a website follows a Poisson process. Hits occur at the rate of 2.2 per minute between 7:00 P.M. and 10:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 7:42 P.M. and 7:50 P.M. Interpret each result. (a) exactly eight (b) fewer than eight (c) at least eight
- Calculate each Poisson probability: (a) P(X=2), λ = 0.10 (Round your answer to 7 decimal places.) ProbabilityRecall that 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. Now 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 = 220 numerical entries from the file and r = 49 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. A) What is the value of the sample test statistic? (Round your answer to two decimal places.)B) Find the P-value of the test statistic. (Round your answer to four decimal places.)Recall that 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. Now 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 = 220 numerical entries from the file and r = 49 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.