3. The discrete random variable \(X\) is distributed \(\mathrm { B } ( n , p )\).
- Write down the value of \(p\) that will give the most accurate estimate when approximating the binomial distribution by a normal distribution.
- Give a reason to support your value.
- Given that \(n = 200\) and \(p = 0.48\), find \(\mathrm { P } ( 90 \leq X < 105 )\).