Question

In eight throws of a die, 5 or 6 is considered a success. Find the mean number of successes and the standard deviation.

Answer 1

Let X denote the number of successes in 8 throws.
n =8 
p = probability of getting 5 or 6 =

\[\frac{2}{6} = \frac{1}{3} \text{ and } q = \frac{2}{3}\]

\[\text{ Mean }  (np) = \frac{8}{3}\]

\[\text{ Variance } (npq) = \frac{16}{9}\]

\[\text{ Standard deviation } = \sqrt{\text{ Variance} } = \frac{4}{3}\]

\[\text{ So, mean = 2 . 66 and standard deviation } = 1 . 33\]