Question 1151341
fewer than 3 is 0,1,2
for 0 this is 1*0.2^0*0.8^8=0.1678
for 1 this is 8*0.2*0.8^7=0.3355
for 2 this is 8C2*0.2^2*0.8^6=0.2936
0.7969


mean is 80*.20 or 16  np and p is 0.2
variance is np(1-p) or 16*.8=12.8
sd is sqrt(V)=3.58

fewer than 30 is using continuity correction factor is z<(29.5-16)/3.58 or <3.77 or essentially 100%.
As the sample size increases, the error from the mean decreases. It is quite likely to have outliers with a small sample; it is far less likely (1/ sqrt(n)) to have the same error with a larger sample size.

what is the probability none is type A? That is 0.8^20=0.0115
The complement, 1-0.0115 or 0.9885 is the probability at least one is type A.
normal approximation: mean is 20*0.2 or 4
V is 4(0.8)=3.2
sd is sqrt(3.2)=1.79
for at least 1 what is probability z> (0.5-4) / 1.79 (continuity correction factor)
or z>-3.5/1.79 or 0.9747