Question

Recent crime reports indicate that 16.9 motor vehicle thefts occur every hour in Canada. Assume that the distribution of thefts per hour can be approximated by a Poisson probability distribution.

a. Calculate the probability exactly four thefts occur in an hour.(Round the final answer to 5 decimal places.)

Probability           

b. What is the probability there are no thefts in an hour? (Round the final answer to 5 decimal places.)

Probability           

c. What is the probability there are at least 20 thefts in an hour? Use excel or online calculator to find the answer. (Round the final answer to 5 decimal places.)

Probability  

Answer 1

here we use poisson distribution with parameter =16.9 and for poisson distribution

P(X=x)=exp(-)^^x/x!

(a)P(X=4)=exp(-16.9)*(16.9)^4/4!=0.00016 ( using ms-excel=poisson(4,16.9,0))

(b)P(X=0)=exp(-16.9)*(16.9)^0/0!=0.00000 ( using ms-excel=poisson(0,16.9,0))

(c)P(at least 20 theft)=P(X>=20)=1-P(X<20)=1-P(X<=19)=1-0.74441=0.25559 ( ( using ms-excel=poisson(19,16.9,1))