Use the normal dist to approx the desired prob. Find the prob of getting at most 30 fives in 200 tosses of a fair 6 sided die

Answer 1

Mean = np
SD = √npq

n = 200
p = 1/6
q = 1 - p = 5/6

Therefore:
Mean = 200(1/6) = 33.33
SD = √[200(1/6)(5/6)] = 5.27

Use z-scores:
z = (x - mean)/SD

z = (30 - 33.33)/5.27 = -0.63

Check a z-table for the probability.
(Remember the problem is asking "at most 30" when looking at the table.)