Assume a Poisson distribution with 2 = 5.7. Find the following probabilities. a. X = 1 b. X 1 d. Xs1Assume that the number of new visitors to a website in one hour is distributed as a Poisson random variable. The mean number of new visitors to the website is 2.9 per hour. Complete parts (a) through (d) below. a. What is the probability that in any given hour zero new visitors will arrive at the website? b. What is the probability that in any given hour exactly one new visitor will arrive at the website? c. What is the probability that in any given hour two or more new visitors will arrive at the website? cl. What is the probability that in any given hour fewer than three new visitors will arrive at the website? Over a period of three months during one year, an airline's rate of involuntarily denying boarding was 0.97 per 10,000 passengers. Complete parts (a) through (0) below. a. What is the probability that in the next 10,000 passengers, there will be no one involuntarily denied boarding? b. What is the probability that in the next 10,000 passengers, there will be at least one person involuntarily denied boarding? c. What is the probability that in the next 10,000 passengers, there will be at least two persons involuntarily denied boarding? A company publishes statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For one year, CarA had 1.37 problems per car. Let the random variable X be equal to the number of problems with a newly purchased model A car. Complete parts (a) through (d). b. Making the assumptions as in (a), if you purchased a model A car, what is the probability that the new car will have zero problems? 0. Making the assumptions as in (a), if you purchased a model A car, what is the probability that the new car will have two or fewer problems? Two students have started a business to seal driveways during the summer months. They rent a pickup truck and a power sprayer. With this they will use a tar based spray to seal asphalt driveways. Past experience has shown that the best time to sign up customers is to ring their doorbells between 5:00 and 8:00 pm. on any weekday evening. Any jobs that they obtain will be completed the next day. In the months of June, July and August they find that they get an average 2 customers per hour ringing doorbells. PLEASE USE 4 DECIMAL PLACES IN THE ANSWERS. E) a) What is the probability that they will get from 5 to 9 jobs in an evening of soliciting? The probability that they will get from 5 to 9 jobs in an evening of soliciting is D. b) They charge $25 per driveway. If the truck costs $50 per day. and the spraying equipment costs $20 per day and the material to seal one driveway costs $5, what is the probability that they will make a prot on any given day. The probability that they will make a prot on any given day is D