Question

if i have a 4/5 = .80 probability of winning a game of solitaire.

How many games do I have to play before I can use the CLT to reasonably approximate the sampling distribution of the sample proportion of wins?

Answer 1

Let be the probability of winning the game.

Let n be the number of games one have to play to use CLT.

Because the normal approximation of binomial distribution ( which is the CLT for sample proportion) is not accurate for small values of n, a general rule is to use the normal approximation only if np and n(1 – p) are greater than or equal to 10

So in the given problem,

Hence for , if the number of games more than or equal to 50, one can use CLT to approximate the sampling distribution of sample proportion of wins.

So the minimum number of games one have to play before using CLT is 50.