The discrete random variable X X\,X has the distribution X∼B(20,0.41)X \sim B(20, 0.41)X∼B(20,0.41).
Find P(3<X≤7)P(3 < X \le 7)P(3<X≤7).
A transport survey records that 30% of commuters usually travel by bus. After a route change, a random sample of 50 commuters is taken, and 9 of them usually travel by bus. Stating your hypotheses clearly, test at the 5% significance level whether the proportion of commuters travelling by bus has decreased.