The Poisson distribution is P(X=x)=(e^-µ)(µ^x)/x! where µ=expected or average number of occurrences (µ=3 in this case) of an event and x is the discrete number of occurrences for which we want the probability. The sum total of all probabilities is 1. If we put x=0, then we want the specific probability of there being no occurrences.
P(0)=e^-3=0.05 approx. So the probability of some policy sales is 1-0.05=0.95 (a).
(b) For ≥2 and <5 we want the sum of X=2, X=3, X=4. P(2)+P(3)+P(4)=0.2240+0.2240+0.1680=0.616.
(c) If the average per week is 3 policies sold, then the daily average is 3/5=0.6, so µ=0.6 and X=1:
P(1)=e^-0.6*0.6=0.33 approx.