The random variable X X\,X has the distribution X∼B(n,0.25)X \sim B(n, 0.25)X∼B(n,0.25), and
P(X=0)<0.01P(X = 0) < 0.01P(X=0)<0.01
Show that n>log0.01log0.75\displaystyle n > \frac{\log 0.01}{\log 0.75}n>log0.75log0.01.
Find the smallest possible value of nnn.
For this value of nnn, find the mean and the variance of XXX.
For this value of nnn, find P(X≥4)P(X \ge 4)P(X≥4).
39 exam-style questions on AQA A Level Maths 2.4.1 Discrete distributions and the binomial. Each one has a worked solution and a mark scheme showing where the marks go.