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.

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


2) Assume a normal distribution with mean = 28.2, stdev = 4.8

Look up z-value in normal table to find probability.

Hope that helps.

Teri ma ki chhut‌‌‌‌‌‌