Homework Soursesuppose it is known from large amounts of historical data th
suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period is characterized by the following discrete probability function: f(x)= e^-6 (6^x/x!), for x=0,1,2,......
(a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
(b) Find the probability that only 2 cars arrive.
Please show how to solve with work, Thank You
suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period is characterized by the following discrete probability function: f(x)= e^-6 (6^x/x!), for x=0,1,2,......
(a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
(b) Find the probability that only 2 cars arrive.
Please show how to solve with work, Thank You
suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period is characterized by the following discrete probability function: f(x)= e^-6 (6^x/x!), for x=0,1,2,......
(a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
(b) Find the probability that only 2 cars arrive.
Please show how to solve with work, Thank You
Solution
Note that
P(more than 8) = 1 - P(at most 8)
Thus, as this is a Poisson Distribution of mean = 6, using a cumulative Poisson table or technology,
P(at most 8) = 0.847237494
Thus,
P(more than 8) = 0.152762506 [ANSWER]
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Plugging in x = 2 to the formula given f(x), where e = 2.71828,
P(2) = 0.044617539
