Question

Suzan is taking part in five competitions. The probability of her winning any competition is 0.4. (a) Find the probability of her winning at most two competitions. (3 marks) (b) Find the average and standard deviation of this distribution (3 mark

Answer 1

Let X be a random variable representing the number of winning competitions, then X ~ BIN(5, 0.4)

a) $P(X≤2)=P(X=0)+P(X=1)+P(X=2)={5 \choose 0}*0.4^0*0.6^5+{5 \choose 1}*0.4^1*0.6^4+{5 \choose 2}*0.4^2*0.6^3=0.68256$

б) $E(X)=5*0.4=2$

$\sigma(X)=\sqrt{5*0.4*0.6}=\sqrt{1.2}\approx1.095$