let say 20% percent of americans used the emergency room last year. Now if I choose 17 people at random find the probability that 6 of them used the emergency room last year. Also finf the probability that at least 5 used the emergency room last year. Finally find the mean and the variance of this experiment.

Think binomial probability.

Exactly 6:

C(17,6)(0.20)^{6}(0.80)^{11}

At least 5:

\sum_{k=5}^{17}C(17,k)(0.20)^{k}(0.80)^{17-k}