The number of arrivals at a car wash is Poisson distributed with a mean of 10.5

Question

The number of arrivals at a car wash is Poisson distributed with a mean of 10.5 per hour.

(a) Calculate by hand the probability that exactly 10 cars will arrive in the next hour of operation.

(b) Use EXCEL to calculate the probability that exactly 8 cars will arrive in the next hour of operation.

(c) Use EXCEL to calculate the probability that 6 or fewer cars will arrive in the next hour of operation.

(d) Use EXCEL to calculate the probability that more than 15 cars will arrive in the next hour of operation.

Explanation / Answer

mean is 10.5

a) P(x=10)=(e^(-mean))(mean^x)/x! = exp(-10.5)*(10.5^10)/10! =0.1236

b) P(x=8)=POISSON.DIST(8,10.5,FALSE)=0.1009

c) P(x<=6)=POISSON.DIST(6,10.5,TRUE)=0.1016

d) P(x>15)=1-P(x<=15)=1-POISSON.DIST(15,10.5,TRUE)=0.0683

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