Here's my problem:

In a large population, 12.5% of all individuals have diabetes.

(a) Seven of these individuals are sampled at random. What is the probability

that two or more sampled individuals have diabetes?

(b) Seven hundred of these individuals are sampled at random. What is the

probability that eighty or fewer have diabetes? (Use a convenient approxi-

mation and justify it)

I solved a) using the binomial distribution and calculating 1-P(X=1)-P(X=0).

But I am not sure that is how you do it.

For b) I suppose I have to go with the central limit theory, but I have no idea how to apply it.

Can you help out, please?

I have been browsing for hours looking for some solved examples like this but I haven't found anything yet.

Thank you!