3.126 Refer to Exercise 3.122. Assume that arrivals occur according to a Poisson process with an average of seven per hour. What is the probability that exactly two customers arrive in the two-hour period of time between a 2:00 P.M. and 4:00 P.M. (one continuous two-hour period)? b 1:00 P.M. and 2:00 p.M. or between 3:00 P.M. and 4:00 p.M. (two separate one-hour periods that total two hours)?
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- Determine if the following scenarios follow a Poisson distribution or do not follow a Poisson Distribution. • You work in a shoe shop and you want to find the distribution of the total number of people who come into the store in a day. You also observe that there are usually more people who come into the shop over lunchtime (10-2 pm) and more people who come into the store after they finish work (5 pm-6 pm). Let X be the number of people who come into the shoe shop on a given day. No - not Poisson • You love peanut butter and want to know how many people buy peanut butter from Trader Joe's. One summer you have nothing to do so you go and stand in Trader Joe's every day and count how many people buy peanut butter in a given week. You assume that consumers do not impact each other's decisions. Let Y be the number of people who buy peanut butter in a given week. Yes - Poisson You want to know how many people in a group of 100 take painkillers if they have a headache. You think that the…A sample of a radioactive material is studied in a lab. There are 741 gamma ray emissions over 130 seconds. Use the Poisson distribution to find the probability that 1 or fewer gamma rays are emitted in a given second. Do not round intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.) ?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
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- Top Cutz International Barbershop is a popular haircutting and styling salon . Four barbers work full-time and spend an average of 15 minutes on each customer. Customers arrive all day long at an average rate of 12 per hour. When they enter, they take a number to wait for the first available barber. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed. REQUIRED (c) What is the average time spent in the shop?The number of hits to a website follows a Poisson process. Hits occur at the rate of 6.8 per minute between 7:00 P.M. and 11:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 10:13 P.M. and 10:14 P.M. Interpret each result. (a) exactly seven (b) fewer than seven (c) at least seven ..... (a) P(7) = (Round to four decimal places as needed.) On about of every 100 time intervals between 10:13 P.M. and 10:14 P.M, the website will receive hit(s). (Round to the nearest whole number as needed.) (b) P(x <7)=| (Round to four decimal places as needed.) On about of every 100 time intervals between 10:13 P.M. and 10:14 P.M, the website will receive hit(s). (Round to the nearest whole number as needed.) (c) P(x27) = (Round to four decimal places as needed.) On about of every 100 time intervals between 10:13 P.M. and 10:14 P.M, the website will receive hit(s). (Round to the nearest whole number as needed.) Time Remaining:…A reservation service employs five information operators who receive requests for information independently of one another, each according to a Poisson process with rate λ = 3 per minute. What is the probability that during a given 1-minute period, exactly one of the five operators receive no requests?