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 P(X=2)P(X=2)P(X=2).
For this value of nnn, find P(X≥4)P(X \ge 4)P(X≥4).
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.