Cars arrive at a car wash randomly and independently; the probability of an arri

Question

Cars arrive at a car wash randomly and independently; the probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 11 cars per hour. Write down the name of the distribution and parameter value(s) you used for each question (i.e., what table was used).

a. What is the probability that at most 20 cars will arrive during the next two hours of operation?

b. What is the probability that more than 22 cars will arrive during the next two hours of operation?  

Explanation / Answer

Cars arrive at a car wash randomly and independently; the probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 11 cars per hour. Write down the name of the distribution and parameter value(s) you used for each question (i.e., what table was used).

Poisson distribution is used.

The mean arrival rate is 11 cars per hour

The mean arrival rate is 22 cars per two hours.

Poisson mean parameter =22 is used.

a. What is the probability that at most 20 cars will arrive during the next two hours of operation?

P( x 20) = 0.3869

b. What is the probability that more than 22 cars will arrive during the next two hours of operation?  

P( x >22) = 0.4436

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