Before seeing the theorem for this case, you should know that there is a rule of thumb to know if the theorem will hold or not for the Binomial distribution case. This condition is the following:

if 𝑚𝑖𝑛(𝑁𝑝,𝑁(1−𝑝))>=5 then CLT holds

where 𝑁 = 𝑛 ∗ 𝑠𝑎𝑚𝑝𝑙𝑒_𝑠𝑖𝑧𝑒

What is N, n, and sample_size refer to here?