Question

The average number of traffic accidents on a certain section of highway is two
per week.
a. Find the probability that three or more accidents happen during a one-week
period.

b. Find the standard deviation for the number of traffic accidents.

Answer 1

Let X be a number of accidents on highway

Probability mass function of X is,

a) We want to find, P(X >= 3)

P(X >= 3)

= 1 - P(X < 3)

= 1 - P(X <= 2)

= 1 - POISSON(2, 2, 1) [ Excel commad ]

= 0.32332356

=> P(X >= 3) = 0.3233 ( rounded to 4 decimal places)

Therefore, the probability that three or more accidents happen during a one-week period is 0.3233

b) Standard deviation of X is,

Therefore,  the standard deviation for the number of traffic accidents is 1.4142