Question

Each entry in a table of random digits like Table $\mathrm{D}$has probability $$ of being a 0 , and the digits are independent of one another. Each line of Table D contains 40 random

digits. The mean and standard deviation of the number of 0 s in a randomly selected line will be approximately

a. mean $=0.1$, standard deviation $=0.05$.

b. mean $=0.1$, standard deviation $=0.1$.

c. mean $=4$, standard deviation $=0.05$.

d. mean $=4$, standard deviation $=1.90$.

e. mean $=4$, standard deviation $=3.60$.

Short answer

The correct option is (d)

Step-by-step solution

Given Information

Probability of success $\left(p\right)=0.1$

Number of trials$\left(n\right)=4$

Explanation for correct option

The mean and standard deviation can be calculated as:

$$\begin{gathered} \mu =n\times p \\ =40(0.1) \\ =4 \\ \sigma =\sqrt{n\times p\times (1-p)} \\ =\sqrt{40(0.1)(1-0.1)} \\ =1.9 \end{gathered}$$

The mean and standard deviation are 4 and $1.9$respectively.

Hence, the correct option is (d).