Question

Check my steps and for part b, the professor wants us to show are work and I don't know how to solve it by hand.

Answer 1

Part a is correct.

Part b can be done a couple ways.
1) Use binomial distribution. p = 0.2, n = 144
P(x>3) = 1 - P(x=0) -p(x=1) -p(x=2) -p(x=3)
where
$P(x=k) = (nCk)p^k (1-p)^{n-k}$

2) Assume a normal distribution with mean = 28.2, stdev = 4.8
$z = \frac{4 - 28.2}{4.8} = -5.04$
Look up z-value in normal table to find probability.

Hope that helps.