Question

4.3 car accidents occur on certain highway each month on average. Answer:

a. In the next month, what is the probability that at most 2 accidents happen?

b. In a particular month, what is the probability that no accidents will happen in the first 10 days?

(d) Considering next year, let Z denote the number of months in which there will be no car accidents on the highway. What distribution does Z have? Be sure to specify both the distribution name and parameter value(s).

c. For a particular year, if total number of months in which an accident doesn't occur is A, what kind of distribution will it have? Also give its parameters.

Answer 1

a) if N= no. of car accidents in a month then N follows a Poisson(3) distribution. Thus the probability that at most 2 accidents happen in next month is P(N2) = 0.4232

b) If N1= no. of car accidents in 10 days then N1 follows a Poisson(1) distribution. Thus the probability that no accidents will happen in the first 10 days is P(N1=0) = 0.3679

c) In a month the probability that an accident doesn't occur is given by P(N1) = 0.8506. Thus if A= total number of months in which an accident doesn't occur. Then A follows a Binomial distribution with n=12 and p=0.8506

d) In a month the probability that no accident occurs is 0.0498. Thus if Z = the number of months in which there will be no car accidents on the highway. then Z follows a Binomial distribution with n=12 and p=0.0498.