Question 3 A sales firm receives an average of three calls per hour on its toll-free number. Suppose you were asked to find the probability that it will receive at least three calls, in a given hour: (a) (i) which distribution does this scenario fit and why? (ii) define the variable of interest, X. (iii) what are the possible values of X? (b) What is the probability that in a given hour it will receive at least three calls?

a)

i) it is a poisson distribution. This is so because it defines the probability of a number of independent events occurring in a fixed time. It shows how many times an event is likely to occur over a specified period.

ii) x is a poisson variable with mean = 3, so the probability mass function of of x is

p(X=x) = (e-3 * 3x)/(x!), x= 0,1, 2,3, ......

iii) The possible values of x are 0,1,2,3,4 ....

iv) we define p(x≥3) = 1- p(x=0) - P(x=1) - P(x=2)

= 1- ( (e-3 *30) - (e-3 * 31) - ( (e-3 * 32) /2) )

=0.5767 which is the required solution.