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.)
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
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