4 The records at a passport office show that, on average, 15 per cent of photographs that accompany applications for passport renewals are unusable.
Assume that exactly one photograph accompanies each application.
- Determine the probability that in a random sample of 40 applications:
- exactly 6 photographs are unusable;
- at most 5 photographs are unusable;
- more than 5 but fewer than 10 photographs are unusable.
- Calculate the mean and the standard deviation for the number of photographs that are unusable in a random sample of \(\mathbf { 3 2 }\) applications.
- Mr Stickler processes 32 applications each day. His records for the previous 10 days show that the numbers of photographs that he deemed unusable were
$$\begin{array} { l l l l l l l l l l }
8 & 6 & 10 & 7 & 9 & 7 & 8 & 9 & 6 & 7
\end{array}$$
By calculating the mean and the standard deviation of these values, comment, with reasons, on the suitability of the \(\mathrm { B } ( 32,0.15 )\) model for the number of photographs deemed unusable each day by Mr Stickler.