5 The probability that a new car of a certain type has faulty brakes is 0.008 . A random sample of 520 new cars of this type is chosen, and the number, \(X\), having faulty brakes is noted.
- Describe fully the distribution of \(X\) and describe also a suitable approximating distribution. Justify this approximating distribution.
- Use your approximating distribution to find
(a) \(\mathrm { P } ( X > 3 )\),
(b) the smallest value of \(n\) such that \(\mathrm { P } ( X = n ) > \mathrm { P } ( X = n + 1 )\).