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.
390 exam-style questions on AQA A Level Maths 2.4 N: Statistical distributions, covering 2.4.1 Discrete distributions and the binomial, 2.4.2 The Normal distribution (A-level only), and 2.4.3 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.