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Question
In eight throws of a die, 5 or 6 is considered a success. Find the mean number of successes and the standard deviation.
Solution
Let X denote the number of successes in 8 throws.
n =8
p = probability of getting 5 or 6 =
\[\frac{2}{6} = \frac{1}{3} \text{ and } q = \frac{2}{3}\]
\[\text{ Mean } (np) = \frac{8}{3}\]
\[\text{ Variance } (npq) = \frac{16}{9}\]
\[\text{ Standard deviation } = \sqrt{\text{ Variance} } = \frac{4}{3}\]
\[\text{ So, mean = 2 . 66 and standard deviation } = 1 . 33\]
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