Suppose that the number of cars arriving at a busyintersection in a large city h

Question

Suppose that the number of cars arriving at a busyintersection in a large city has a Poisson distribution with mean120. Determine a lower bound for the probability that the number ofcars arriving in a given 20-minute period will be between 100 and140 using Chebyshev's inequality. Will rate highest Suppose that the number of cars arriving at a busyintersection in a large city has a Poisson distribution with mean120. Determine a lower bound for the probability that the number ofcars arriving in a given 20-minute period will be between 100 and140 using Chebyshev's inequality. Will rate highest

Explanation / Answer

Since this is Poisson, you know the variance = mean = 120. SinceChebshev deals with standard deviations, take the square root ofthe variance to obtain the s.d. = 10.955. Since 120-100= 20, dividethis by your standard deviations to get 1.82565. Plug this into Chebyshev's inequality, to get 1/(1.82)^2, to get.3000. Your lower bound is (120-.30(120)) or 84. 84 is your lowerbound, and since you know poisson is symmetric, 36+120 = 156 isyour upper bound (in case you need it)

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