Question

8. The city of Fastville has been experiencing a mean of 73 car accidents per year.

1) Find the probability that on a given day the number of car accidents in Fastville is 2. (Assume 365 days in a year.) Round your answer to four decimal places.

2) Find the probability that on a given day the number of car accidents in Fastville is more than one. Round your answer to four decimal places.

3) Find the minimum and the maximum usual values for the number of car accidents per week. Is it unusual to have no accidents in a given week in Fastville? Note: you must briefly explain your answer, no points will be given for a simple 'yes' or 'no'. Please answer all with the work!! THANK YOU!!!

Answer 1

mean of 73 car accidents per year = 73/365 accidents /day

1)

Mean/Expected number of events of interest: λ = 73/365 = 0.20

poisson probability distribution

P(X=x) = e-λλx/x!

P ( X =    2   ) = e^-0.2*0.2^2/2!=   0.0164  

2) P(more than one) = P(X>1) = 1 - P(x=0) - P(X=1) = 1-0.8187 - 0.1637 = 0.0175

3)

variance = λ   0.2
std dev = √λ =    0.4472

usual range = µ±2σ = (0.2±2*0.4472) = (-0.694 , 1.094 )

since, 0 lies within the usual range, so,

No, it is not unusual to have no accidents in a given week in Fastville