Question

The number of accidents on a particular highway average 4.4 per year.

Answer 1

It is given that number of accidents on a particular highway is average 4.4 per year.

a. Let X be the number of accidents on a particular highway.

X follows Poisson distribution with mean μ =4.4

The probability function of X , Poisson distribution is given by;

P(X=k) = $\frac{e^{-4.4} (4.4)^{k}}{k!}$

b. Probability that there are exactly four accidents next year, X=4

P(X=4) = $\frac{e^{-4.4} (4.4)^{4}}{4!}$

P(X=4) = 0.1917

Probability that there are exactly four accidents next year is 0.1917

c. Probability that there are more that three accidents next year is

P(X > 3) = 1 - P(X ≤ 3)

= 1 - [ P(X=3) + P(X=2) + P(X=1) + P(X=0)]

P(X=3) = $\frac{e^{-4.4} (4.4)^{3}}{3!}$

P(X=3) = 0.1743

P(X=2) = $\frac{e^{-4.4} (4.4)^{2}}{2!}$

P(X=2) = 0.1188

P(X=1) = $\frac{e^{-4.4} (4.4)^{1}}{1!}$

P(X=1) = 0.054

P(X=0) = $\frac{e^{-4.4} (4.4)^{0}}{0!}$

= 0.0122

Using these probabilities into above equation

P(X > 3) = 1 - P(X ≤ 3) = 1 - [ P(X=3) + P(X=2) + P(X=1) + P(X=0)]

= 1 - (0.1743 + 0.1188 + 0.054 + 0.0122)

P(X > 3) = 1 - 0.3593

P(X > 3) = 0.6407

Probability that there are more than three accidents next year is 0.6407