5 A spinner has 5 edges. Each edge is numbered with a different integer from 1 to 5 . When the spinner is spun, it is equally likely to come to rest on any one of the edges. The spinner is spun 100 times. The number of times on which the spinner comes to rest on the edge numbered 5 is denoted by \(X\).

1. \(\mathrm { E } ( X )\),
2. \(\operatorname { Var } ( X )\).
   1. Write down
   2. Use a normal distribution with the same mean and variance as in your answers to part (i) to estimate the smallest value of \(n\) such that \(\mathrm { P } ( X \geqslant n ) < 0.02\).
   3. Use the binomial distribution to find exactly the smallest value of \(n\) such that \(\mathrm { P } ( X \geqslant n ) < 0.02\). Show the values of all relevant calculations.