Question

On average, Chance has noticed that 19 trains pass by his house daily (24 hours) on the nearby train tracks. What is the probability that at most 6 trains will pass his house in a 8-hour time period? (Round your answer to three decimal places.)

Answer 1

Answer:

0.470

Step-by-step explanation:

Given that on  average, Chance has noticed that 19 trains pass by his house daily (24 hours) on the nearby train tracks.

For 8 hour period the average would be 19/3

X no of trains passing is Poisson with average 19 trains per hour

P(X=x) = $\frac{19^x e^{-19} }{x!}$

Required probability = the probability that at most 6 trains will pass his house in a 8-hour time period

=the probability that at most 6*3 trains will pass his house in a 8*3-hour time period

=P(X$\leq$18)

=0.4695

=0.470