5 The random variable \(W\) has the distribution \(\mathbf { B } ( 30 , p )\).
- Use the exact binomial distribution to calculate \(\mathbf { P } ( W = 10 )\) when \(p = 0.4\).
- Find the range of values of \(p\) for which you would expect that a normal distribution could be used as an approximation to the distribution of \(W\).
- Use a normal approximation to calculate \(\mathrm { P } ( W = 10 )\) when \(p = 0.4\).