Question

the table below shows the probability distribution of a random variable x.

x	p(x)
-12	0.27
-11	0.21
-10	0.52

what is the standard deviation of x?
round your answer to the nearest hundredth.

Explanation:

Step1: Calculate the expected value $E(X)$

$E(X)=\sum_{i}x_ip_i=(- 12)\times0.27+(-11)\times0.21+(-10)\times0.52=-10.73$

Step2: Calculate the variance $Var(X)$

$Var(X)=\sum_{i}(x_i - E(X))^{2}p_i$
$=((-12)-(-10.73))^{2}\times0.27+((-11)-(-10.73))^{2}\times0.21+((-10)-(-10.73))^{2}\times0.52$
$=(-1.27)^{2}\times0.27+(-0.27)^{2}\times0.21+(0.73)^{2}\times0.52$
$=1.6129\times0.27 + 0.0729\times0.21+0.5329\times0.52$
$=0.435483+0.015309 + 0.277108$
$=0.7279$

Step3: Calculate the standard deviation $\sigma$

$\sigma=\sqrt{Var(X)}=\sqrt{0.7279}\approx0.85$

Answer:

$0.85$