Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a

Question

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Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a

Poisson distribution with parameter μ = 20 (suggested in the article "Dynamic Ride 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 15? (b) What is the probability that the number of drivers will exceed 26? (c) What is the probability that the number of drivers will be between 15 and 26, inclusive? What is the probability that the number of drivers will be strictly between 15 and 26? (d) What is the probability that the number of drivers will be within 2 standard deviations of the mean value?

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-03-03T11:59:38+03:00

Answer:

Step-by-step explanation:

It has been established that the count of drivers traveling between a specific origin and destination in a certain time frame follows a Poisson distribution with a mean μ = 20 (as indicated in the article "Dynamic Ride Sharing: Theory and Practice"†).

a) $P(X\leq 15) = 0.1565=0.157$

b) $P(X>26) =1-F(26)\\= 1-0.9221\\=0.0779=0.078$

c) $P(15\leq x\leq 26)\\=F(26)-F(14)\\=0.9221-0.1049\\=0.8172=0.817$

d) 2 standard deviations = 2(20) = 40

Thus, this means the range for 2 standard deviations is

20-40, 20+40

which equates to (0,60)

$P(0$