Moderate -0.3 This is a straightforward application of the Poisson approximation to the binomial distribution. Students need to identify n=130, p=1/40, calculate λ=np=3.25, then use P(X=4)=e^(-3.25)×3.25^4/4!. While it requires recognizing when the approximation is appropriate (large n, small p), the calculation itself is routine and follows a standard formula with no conceptual challenges beyond basic substitution.
2 It is given that on average one car in forty is yellow. Using a suitable approximation, find the probability that, in a random sample of 130 cars, exactly 4 are yellow.
2 It is given that on average one car in forty is yellow. Using a suitable approximation, find the probability that, in a random sample of 130 cars, exactly 4 are yellow.
\hfill \mbox{\textit{OCR S2 2007 Q2 [5]}}