63% of men consider themselves baseball fans. You randomly select 10 and ask if he consider him self a baseball fan. Find the probability that the number who consider themselves baseball fans is (a) exactly 8, (b) at least (8) less than (8)

Answer 1

Assuming the random selection is from a large pool of people, in which case the probability remains constant throughout the experiment.
This experiment could then be modeled by the binomial distribution, with probability

P(X=n)=C(N,x)p^x(1-p)^N-x
where p=probability of success = 0.63
N=10 (sample size)

For part (a)
calculate P(X=8)
for part (b),
calculate ΣP(X=i) where i=8,9,10
for part (c),
calculate (1-answer in part (b))
since
ΣP(X=0.....10) = 1