suppose it is known from large amounts of historical data that X, the number of
ID: 3439005 • Letter: S
Question
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
Explanation / Answer
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]
*******************************
Plugging in x = 2 to the formula given f(x), where e = 2.71828,
P(2) = 0.044617539
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