3 In the data-entry department of a certain firm, it is known that \(0.12 \%\) of data items are entered incorrectly, and that these errors occur randomly and independently.
- A random sample of 3600 data items is chosen. The number of these data items that are incorrectly entered is denoted by \(X\).
- State the distribution of \(X\), including the values of any parameters.
- State an appropriate approximating distribution for \(X\), including the values of any parameters.
Justify your choice of approximating distribution.
- Use your approximating distribution to find \(\mathrm { P } ( X > 2 )\).
- Another large random sample of \(n\) data items is chosen. The probability that the sample contains no data items that are entered incorrectly is more than 0.1 .
Use an approximating distribution to find the largest possible value of \(n\).