SOLUTION: A particular experiment consists of rolling a fair six-sided die 200 times and counting the number of occurrences of three dots showing on the upper face. Determine the probabilit

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Question 375604: A particular experiment consists of rolling a fair six-sided die 200 times and counting the number of occurrences of three dots showing on the upper face. Determine the probability that three dots will show on the upper face exactly 40 times.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
C%28200%2C40%29%2A%281%2F6%29%5E40%2A%285%2F6%29%5E160. To get an approximate answer, use the normal approximation to the binomial distribution:
; hence P%28X+%3C=+40.5%29+=+P%28Z+%3C=+1.36%29.
; hence P%28X+%3C=+39.5%29+=+P%28Z+%3C=+1.17%29.
Then the probability is approximately P%28Z+%3C=+40.5%29+-+P%28Z+%3C=+39.5%29 = 0.9131 - 0.8790 = 0.0341.
(Here mu+=+np+=+100%2F3, and sigma+=+sqrt%28npq%29+=+sqrt%28250%2F9%29.)