A major hotel chain keeps record of the number of customer complaints per week. In a recent year, the hotel chain had 5 complaints per week. Assume that the number of complaints follows a Poisson distribution. What is the probability the hotel will receive more than two complaints in the next week?

An auto parts store sells an average of 8.3 oil filters per week. Use the Poisson distribution to find the probability that they sell exactly 6 oil filters in a given week. Do not round intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)

The number of typing errors made by a typist has a Poisson distribution with an average of three and a half errors per page. If five or more errors appear on a given page, the typist must retype the whole page.    What is the probability that the typist makes 3 errors on a page?  What is the probability that a randomly selected page does not need to be retyped?

Power failures occur at an electric plant on average 3 times per year. If we can assume this follows a Poisson distribution, answer the following questions. a. What is the probability that there are 4 power failures in 2021? b. What is the probability that there are no more than 2 power failures in a given year? c. How likely is it that there are at least 3 power failures next year?