Executives in the New Zealand Forestry Industry claim that only 5% of all old sawmills sites contain soil residuals of dioxin (an additive previously used for anti-sap-stain treatment in wood) higher...

Executives in the New Zealand Forestry Industry claim that only 5% of all old sawmills sites contain soil residuals of dioxin (an additive previously used for anti-sap-stain treatment in wood) higher than the recommended level.  If Environment Canterbury randomly selects 20 old saw mill sites for inspection, assuming that the executive claim is correct:

i) Calculate the probability that less than 1 site exceeds the recommended level of dioxin.

ii) Calculate the probability that less than or equal to 1 site exceed the recommended level of dioxin.

iii) Calculate the probability that at most (i.e., maximum of) 2 sites exceed the recommended level of dioxin.