Answer to Question #264114 in Statistics and Probability for Nathan

Question

During peak traffic periods, accidents occur in a certain small city at a rate of 4.9 per hour. The morning peak lasts for 1.6 hours. On any given day, the probability that there will be at most 2 accidents during the morning peak period is

Answer 1

The probability that there will be at most 2 accidents during the morning peak period is:

$P(X\eqslantless2)=P(X=0)+P(X=1)+P(X=2)$

$P(X\eqslantless2)=\frac{1.6^{0}*e^{-1.6}}{0!}+\frac{1.6^{1}*e^{-1.6}}{1!}+\frac{1.6^{2}*e^{-1.6}}{2!}$

$P(X\eqslantless2)=0.2019+0.3230+0.2584=0.7834$

There is 78.34% probability of that there will be at most 2 accidents during the morning peak period.