I'm not very happy with this problem statement. The independence of the samples is dubious, at best. Plus, is the sample 20 or 200? That will make a difference. Further, we know nothing of the size of the population, excepting that it is likely to be lass than 6 billion. It would be unwise to make conclusions that tell us a sample of 20 or 200 gives THE mean or variance.
In any case. Each experiment is Bernoulli. The entire experiment is Binomial with p = 0.8 and n = 20.
The Population data are given (or are they?):
Population Mean: 20*0.8
Population Variance 20*0.8*0.2
The Sample data are a little sketchy:
Sample Mean: ??? I don't see where we are told this.
Sample Variance This either...
If the problem MEANS (it certainly doesn't SAY so) that p = 0.80 was determined by the sample of 20, then we have an entirely different problem and I have to go with your teacher's response.
The Population data are NOT given:
Population Mean: ??
Population Variance ??
The Sample data are given:
n = 20
p = 0.80
Sample Mean: 20*0.80
Sample Variance: (20*0.8*0.20)/(20*20)
You should be able to calculate the probability in b. Is 200 sufficiently large for a normal approximation?