The probability that a component produced by a machine is faulty is 0.05, independently of every other component. A random sample of n n\,n components is taken.
The probability that the sample contains at least one faulty component is greater than 0.9.
Show that 0.95n<0.10.95^n < 0.10.95n<0.1.
Find the smallest possible value of nnn.
State one assumption needed for the binomial model to be appropriate here.
47 exam-style questions on WJEC A Level Maths 2.4 Statistical distributions, covering 2.4.1 Statistical distributions, 2.4.2 Statistical distributions, and 2.4.3 Statistical distributions. Each one has a worked solution and a mark scheme showing where the marks go.