Little problem that I'm struggling to solve...

The proportion of smokers in a certain population is 25%. What is the probability
that smokers' proportion in a sample of 40 people randomly selected from this
population will be below (strictly less than) 20%.

Surely you would use the binomial table N = 40 P = 0.25 X = 8 (since below 20% = less than 8 people from the sample of 40)

I tried using the binomial table to find P(X<8) then use the binomial equation P(X=8).

So to complete the question I did P(X<8) - P(X=8) = 0.1819.. and I thought 18.19% is the correct answer but I seem to be mistaken? Any help?

The correct answer is 0.2296, why?

Appreciate any help thanks!