- In a large population \(40 \%\) of adults use online banking.
A random sample of 50 adults is taken.
The random variable \(X\) represents the number of adults in the sample that use online banking.
- Find
- \(\mathrm { P } ( X = 26 )\)
- \(\mathrm { P } ( X \geqslant 26 )\)
- the smallest value of \(k\) such that \(\mathrm { P } ( X \leqslant k ) > 0.4\)
A random sample of 600 adults is taken.
- Find, using a normal approximation, the probability that no more than 222 of these 600 adults use online banking.
- Explain why a normal approximation is suitable in part (b)(i)