This seems to be a Binomial problem, where you want

P(X>=20). Here X is bin(48,p)

The p is the probability that a geometric random variable is less than 3.

NOW there are two ways of defining a geo, whether we include he trial on which the first success appears or we don't count that trial. So, I need to know which geo distribution you are using.

Once you obtain the p, just do the usual normal approximation to the binomial AND you should start at 19.5,

using the correction factor.

z=(19.5-np)/(npq)^(1/2)