Question

xP(x)00.2510.0520.1530.55Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

Answer 1

The Solution:

Given:

Required:

Find the standard deviation of the probability distribution.

Step 1:

Find the expected value of the probability distribution.

$E(x)=\mu=\sum_{i\mathop{=}0}^3x_iP_(x_i)$$\begin{gathered} \mu=(0\times0.25)+(1\times0.05)+(2\times0.15)+(3\times0.55) \\ \\ \mu=0+0.05+0.30+1.65=2.0 \end{gathered}$

Step 2:

Find the standard deviation.

$Standard\text{ Deviation}=\sqrt{\sum_{i\mathop{=}0}^3(x_i-\mu)^2P_(x_i)}$$=(0-2)^2(0.25)+(1-2)^2(0.05)+(2-2)^2(0.15)+(3-2)^2(0.55)$$=4(0.25)+1(0.05)+0(0.15)+1(0.55)$$=1+0.05+0+0.55=1.60$

Thus, the standard deviation is 1.60

Answer:

1.60