Question

The proportion of vehicles which drive above the speed limit on a freeway is 78%. Suppose 10 vehicles are randomly clocked. The following is the probability distribution of the number of vehicles which drive above the speed limit. (The blank cells are intentional!)

Answer 1

a) $P(X=x)=n_{C_{x}}(1-p)^{n-x}(p)^{x}$

$P(X=8)=10_{C_{8}}(1-0.78)^{10-8}(0.78)^{8}=45(0.22)^{2}(0.78)^{8}=0.2984$ C

b) $P(X\leq 8)=1-P(X=9)-P(X=10)=1-0.2351-0.0834=0.6815$ C