Consider a binomial experiment with n = 8 trials and p = 0.20. a. find the mean and the standard deviation of the distribution. b. would it be unusual to obtain 5 or more successes

A. np is the mean=8×0.20=1.60; variance=np(1-p)=1.60×0.80=1.28. Standard deviation=√variance=1.13 approx.
b. The coefficients for n=8 are: 1, 8, 28, 56, 70, 56, 28, 8, 1.
The first 4 of these are involved in getting 5 or more successes. Let q=1-p. p=0.20 and q=0.80.
So we have p⁸+8p⁷q+28p⁶q²+56p⁵q³=0.0104... This is a very low probability, so it would be unusual to obtain 5 or more successes.