Customers checking out at Food Tiger arrive in a single-line queue served by two cashiers at a rate of 9 per hour according to a Poisson distribution. Each cashier processes customers at a rate of 7 per hour according to an exponential distribution. (a) If, on average, customers spend 31 minutes shopping before getting in the checkout line, what is the average time (in minutes) a customer spends in the store? (Round your answer to two decimal places.)  ______ minutes (b) What is the average number of customers waiting for service in the checkout line? (Round your answer to four decimal places.)  ______ customers (c) What is the probability that a customer must wait? (Round your answer to four decimal places.)

Describe the distribution where radioactive particles are emitted at a poisson rate of 5 per second. Let W reflect the waiting time until the 20th particle. What is the expected time here?

Data documented for weather events in the state of Montana is obtained over a period of years and includes hail storms causing property damage. The data is analyzed and appears to fit a poison distribution with an average of 3.3 damaging hail storms per year.  What is the likelihood that between 2 and 4 damaging hail storms are seen in a randomly selected year?  please show using Poisson.dist function  What is the probability that at least one significant hail storm causing damage is experienced in the coming year?  What is the likelihood that Montana would experience between 5 and 7 damaging hailstorms over a two year period?  What is the likelihood that Montana would experience more than 7 damaging hail storms over a two-year period? please show all steps using excel formulas

An airport has 3 security lines, with each line capable of scanning 290 people per hour. People arrive in front of the security line at the rate of 850 per hour. Make the standard assumption of a Poisson distribution for arrivals and an exponential distribution for service times, and calculate the following:   What is the probability that there are no people in the waiting line? Answer is NOT 0.02.   What is the average length (number of people) in the waiting line? Answer is NOT 41.52.

The number of industrial injuries per working week in a particular factory is known to follow a Poisson distribution with mean 0.5. Find the probability that in a particular week there will be more than 2 accidents. Express your answer in 4 decimal place value

The number of industrial injuries per working week in a particular factory is known to follow a Poisson distribution with mean 0.5. Find the probability that in a particular week there will be less than 2 accidents. Express your answer in 4 decimal place value

The number of customers arriving at a teller’s window at Commercial Bank is Poisson distributed with a mean rate of 2 persons per minute.   Calculate the probability of three customers arriving in the next 2 minutes?

Suppose that customers arrive at a counter in accordance with a Poisson process with mean rate of 2 per minute (λ = 2/minute). Then the interval between any two successive arrivals follows exponential distribution with mean, 1/λ=1/2 minute. Find the probability that the interval between two successive arrival is,a. more than 1 minuteb. 4 minutes or lessc. between 1 and 2 minutes

Let the breakdown of a machine follow the Poisson process so that the random variable X denoting the number of breakdowns per unit of time is distributed as a Poisson distribution. Then, the time between any two consecutive failures is also a random variable T that is distributed as an exponential with parameter λ. If λ=0.1, what is the probability that the machine will function from 2 to 5 hours before it breaks down again?

The number of industrial injuries per working week in a particular factory is known to follow a Poisson distributionwith mean 0.5. Find the probability that in a three week period there will be no accidents. Express your answer in 3 decimal place value