The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 4.1. Find the probability that exactly 12 road construction projects are currently taking place in this city. Answer:
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- A bank received on average 9 bad cheques per day. What is the probability that the bank will receive 3 bad cheques on any given day. Hint: Use poisson distributionIndustry standards suggest that 12 percent of new vehicles require warranty service within the first year. University Toyota in Morgantown, WV sold 10 Toyotas yesterday. Compute the mean of the probability distribution.According to a survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five. a. What is the probability of receiving no e-mails during an hour (to 4 decimals)? b. What is the probability of receiving at least three e-mails during an hour (to 4 decimals)? For this question, if calculating the probability manually make sure to carry at least 4 decimal digits in your calculations. c. What is the expected number of e-mails received during minutes (to 2 decimals)? d. What is the probability that no e-mails are received during minutes (to 4 decimals)?
- Suppose a set of 100 random numbers is normally distributed, with a mean of 50 and standard deviation 2. What is the probability of leaving the number 50?Assume that your aunt wrote 139 letters to her family members in 2019. Let the random variable x represent the number of these letters that she wrote on a given day. Assume also that this scenario has a Poisson distribution. What is the mean number of letters written per day? Round to 3 decimal places. What is the standard deviation? Round to 3 decimal places.Hits to a high-volume website are assumed to follow a Poisson distribution with a mean of 1200 per day. What is the probability that the number of hits to the website tomorrow will be between 1190 and 1220 (inclusive)?
- An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 115 cm and a standard deviation of 5.5 cm. A. Find the probability that one selected subcomponent is longer than 117 cm. Probability = B. Find the probability that if 4 subcomponents are randomly selected, their mean length exceeds 117 cm. Probability = C. Find the probability that if 4 are randomly selected, all 4 have lengths that exceed 117 cm. Probability =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.The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 4.4 per week. Find the probability of the following events. A. No accidents occur in one week. Probability = B. 7 or more accidents occur in a week. Probability = C. One accident occurs today. Probability =
- The number of content changes to a Web site follows a Poisson distribution with a mean of 0.25 per day. What is the probability of two or more changes in a day? 0.026 0.287 0.267 None of the choicesThe author of a book makes an average of 2 typing errors per page. Find the probability that a randomly selected page from the author's book will have 4 errors. Assume the number of errors per page has a Poisson distribution. Below ?edenotes Euler's number, ?≅2.718