The number of cars arriving at a given intersection follows a Poisson distribution with a mean rate of 4 per second.
a. What is the probability that 3 cars arrive in a given second?
b. What is the probability that 8 cars arrive in three seconds?
c. What is the probability that more than 3 cars arrive in a period of two seconds?
(a) Let X be the number of cars that arrive in a given second. Since the mean rate is 4 per second, X ~ Poisson(4).
(b) Since the mean rate is 4 per second, X ~ Poisson(12)
(c) Since the mean rate is 4 per second, X ~ Poisson(8)
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