pose that the number of drivers who travel between a particular origin and desti
ID: 3074227 • Letter: P
Question
pose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter = 20 (suggested in the article "Dynamic Sharing: Theory and Practice"). (Round your answer to three decimal places.) (a) What is the probability that the number of drivers will be at most 10? (b) What is the probability that the number of drivers will exceed 20? (c) What is the probability that the number of drivers will be between 10 and 20, inclusive? What is the probability that the number of drivers will be strictly between 10 and 20? (d) What is the probability that the number of drivers will be within 2 standard deviations of the mean value?Explanation / Answer
Solution:- Given that = 20
(a) P(X <= 10) = 0.01081 = 0.011
(b) P(X > 20) = 0.44091 = 0.441
(c - 1)
=> P(10 <= X <= 20) = P(X <= 20) - P(X < 10)
= 0.5591 - 0.005
= 0.5541
= 0.554 (rounded)
(c - 2)
=> P(10 < X < 20) = P(X < 20) - P(X <= 10)
= 0.5591 - 0.0108
= 0.5483
= 0.548(rounded)
(d) = 20
For poisson distribution mean = variance
variance = 20
sd = sqrt(20) = 4.4721
There fore:P(Solution:- Given that = 20
(a) P(X <= 10) = 0.01081 = 0.011
(b) P(X > 20) = 0.44091 = 0.441
(c - 1)
=> P(10 <= X <= 20) = P(X <= 20) - P(X < 10)
= 0.5591 - 0.005
= 0.5541
= 0.554 (rounded)
(c - 2)
=> P(10 < X < 20) = P(X < 20) - P(X <= 10)
= 0.5591 - 0.0108
= 0.5483
= 0.548(rounded)
(d) = 20
For poisson distribution mean = variance
variance = 20
sd = sqrt(20) = 4.4721
There fore: P( - 2* < X < + 2*)
: P(20 - (2*4.472) < X < 20 + (2*4.472))
: P(11.056 < X < 28.944)
: P(X < 29) - P(X = 11)
= 0.9657 - 0.0214
= 0.9443
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