Question

(a)

Suppose you are interested in the number of lightning fatalities in Canada. You find that there are an average of 15 fatalities per year due to lightning.

What is the probability that there is 9 to 11 lightning strikes this year (to two decimal places)?

(b)The amount of time (in minutes) that you wait at the for the crosswalk to turn green is anywhere from 9 to 56 seconds. What is the probability that you wait more than 18 seconds? (Write your answer in decimal form to four decimal places.)

(c)

The amount of time (in minutes) that you wait at the for the crosswalk to turn green is anywhere from 5 to 59 seconds. What is the standard deviation (in seconds) for the distribution of the amount of time that you wait for the light to turn green? (Write your answer in decimal form to two decimal places.)

Answer 1

a)

this is Poisson distribution with parameter λ=15

P(9<=X<=11)=P(X=9)+P(X=10)+P(X=11)=

{e-15*159/9!}+{e-15*1510/10!}+{e-15*1511/11!}=

0.1473~ 0.15

b)

P(X>18)=-P(X<18)=1-(18-9)/(56-9)==0.8085

c)

standard deviation =(b-a)/sqrt(12) =(59-5)/sqrt(12)=15.59