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 =$\frac{2}{6}=\frac{1}{3}\mathrm{and}\mathit{}q=\frac{2}{3}$

$$\begin{gathered} \mathrm{Mean}\left(np\right)=\frac{8}{3} \\ \mathrm{Variance}\left(npq\right)=\frac{16}{9} \\ \mathrm{Standard}\mathrm{deviation}=\sqrt{\mathrm{Variance}}=\frac{4}{3} \\ \text{So, m}\mathrm{ean}=2.66\mathrm{and}\mathrm{st}\text{andard}\mathrm{deviation}=1.33 \end{gathered}$$