1 Suppose that 6 is the average number of cars driving throu

1. Suppose that 6 is the average number of cars driving through a particular Dunkin Donuts shop during a 3-minute interval on Monday mornings.

a. Calculate the probability that at most 8 cars show up in a 6-minute time interval.

b. Calculate the probability that 7 or more cars arrive in a 3-minute time interval.

Please explain your process step by step.

a. Calculate the probability that at most 8 cars show up in a 6-minute time interval.

Given X follows Poisson distribution with mean=6*2=12 in 6 minute

P(X=x)=(12^x)*exp(-12)/x!

So P(X<=8) = P(X=0)+P(X=1)+...+P(X=8)

=(12^0)*exp(-12)/1+...+(12^8)*exp(-12)/8!

=0.1550278

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b. Calculate the probability that 7 or more cars arrive in a 3-minute time interval.

Given X follows Poisson distribution with mean=6 in 3 minute

P(X=x)=(6^x)*exp(-6)/x!

So P(X>=7)=1-P(X=0)-P(X=1)-...-P(X=6)

=1-(6^0)*exp(-6)/1-...-(6^6)*exp(-6)/6!

=0.9541777