What is the probability that the shop is empty?
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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
(a) What is the probability that the shop is empty?
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- M3On average, TV crash after 17,000 hours of continuous use. Although the time for the TV to crash is random, researchers have found that the duration until the computer crashes follows an exponential probability distribution. a. What is the probability that the TV will fail with a usage time of less than 17,000 hours?b. What is the probability that the TV will crash with a usage time of more than 17,000 hours?c. What is the probability that no TV will fail after more than 17,000 hours of use?d. What do you think about the results of points b and c above! What is the difference?An Internet celebrity video has an average of 9,000 people watching every day. Try to calculate the probability that no one watches the video for 1 minute using the Poisson distribution and the index distribution respectively.
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- In a recent year, Professor Thompson wrote 195 checks. Find the probability that on a randomly selected day, he wrote at least one check. (Hint: Use the Poisson distribution)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 students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 5 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period. e. Calculate the probability that there will be a failing student within the first semester. F. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?