Question

The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 3.9 per week. Find the probability of the following events.

A. No accidents occur in one week. Probability =

B. 3 or more accidents occur in a week. Probability =

C. One accident occurs today. Probability =

Answer 1

X ~ Poisson( )

Where = 3.9 per week

Poisson probability distribution is

P(X) = e^-X / X!

a)

P( X = 0) = e^-3.9

= 0.02024

b)

P( X >= 3) = 1 - P( X <= 2)  

= 1 - 0.2531 (Probability calculated from cumulative poisson probability table)

= 0.7469

c)

of 1 day = 3.9/7 =

P( X = 1) = e^-3.9/7 * (3.9/7)¹ / 1!

= 0.3192