Cars pass through the automated car wash at the Shell on Carling Avenue at a rate...

 

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Cars pass through the automated car wash at the Shell on Carling Avenue at a rate of 6 cars per hour. The rate at which they pass through the car wash follows a Poisson distribution. You must define a new random variable as appropriate throughout this question. a. Find the probability that exactly 5 cars pass through the car wash in an hour. b. Assuming that the automated car wash at the gas station is open 18 hours a day, what is the expected number of cars that pass through the car wash in a given day? What is the standard deviation for this 18 hour day? c. Joe is supposed to keep an eye on every car that goes through the car wash. As luck would have it, he is the only one working on Saturday afternoon. If he needs to take a 12 minute break, what is the probability that he misses seeing at least one car go through the car wash? Cars pass through the automated car wash at the Shell on Carling Avenue at a rate of 6 cars per hour. The rate at which they pass through the car wash follows a Poisson distribution. You must define a new random variable as appropriate throughout this question. a. Find the probability that exactly 5 cars pass through the car wash in an hour. b. Assuming that the automated car wash at the gas station is open 18 hours a day, what is the expected number of cars that pass through the car wash in a given day? What is the standard deviation for this 18 hour day? c. Joe is supposed to keep an eye on every car that goes through the car wash. As luck would have it, he is the only one working on Saturday afternoon. If he needs to take a 12 minute break, what is the probability that he misses seeing at least one car go through the car wash?

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