The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting $12$ Southwest flights and observing whether they arrive on time.

(a) Find the probability that exactly $7$ flights arrive on time.

(b) Would it be unusual for Southwest to have at least 12 flights arrive on time? ? yes no
(Here "unusual" means "probability < 0.05").

Note: In part (a) enter C(n,k) to stand for the binomial coefficient $\binom{n}{k}=\frac{n!}{k!(n-k)!}$. For example $C(6,2)=15$ is the number of ways of choosing 2 things out of a set of 6 things, if order doesn't count. Don't enter the factorial formula $\displaystyle \frac{n!}{k!(n-k)!}$ if n is large because large factorials are huge and will choke the computer!