X has a binomial distribution B(0.4,35), so:

P(X=n) = 35!/(n! (35-n)!) 0.4^n 0.6^(35-n)

so:

a) P(X=20) = 35!/(20! (15)!) 0.4^20 0.6^15 = 0.016791

b) P(X>=20) = sum_{n=20 to 35} 35!/(n! (35-n)!) 0.4^n 0.6^(35-n) ~= 0.030

c) You should know that the variance of a binomial RV is N p (1-p), so in this case

the variance is 8.4

d) you should know that the mean of a binomial RV is Np, so in this case is 14.

e) Using the normal approx we want the probability that a standard normal RV

exceeds a z score of:

z = (19.5-14)/sqrt(8.4) = 1.90

which is 0.0287.

RonL