Question

Which of the following is the standard deviation of the random variable x

Answer 1

Answer: B. 1.414

Explanation:

let x be the random variable denotes the number of die.

Numbers on 5-faced die = 1,2,3,4,5

Probability of getting any number =
`(1)/(5)`

Mean =
`\bar {x}=\sum p_ix_i`

`\\\\\Rightarrow\bar{x}=(1)/(5)(1)+(1)/(5)(2)+(1)/(5)(3)+(1)/(5)(4)+(1)/(5)(5)\\\\=(1)/(5)(1+2+3+4+5)\\\\=(1)/(5)(15)=3`

Standard deviation:
`\sigma=\sum \sqrt{\frac{(x_i-\bar{x})^2}{N}}`

`=\sqrt{((1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2)/(5)}\\\\=\sqrt{(4+1+0+1+4)/(5)}\\\\=\sqrt{(10)/(5)}\\\\=√(2)\approx1.414`

Hence, the standard deviation of the random variable x is 1.414.

Thus, the correct option is B.