the table below shows the probability distribution of a random variable x.\n|x|p(x)|\n|11|0.3|\n|12|0.5|\n|13…

Explanation:

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

$E(X)=\sum_{i}x_{i}P(x_{i})=11\times0.3 + 12\times0.5+13\times0.2=3.3 + 6+2.6 = 11.9$

Step2: Calculate the variance $Var(X)$

$Var(X)=\sum_{i}(x_{i}-E(X))^{2}P(x_{i})=(11 - 11.9)^{2}\times0.3+(12 - 11.9)^{2}\times0.5+(13 - 11.9)^{2}\times0.2$ $=(- 0.9)^{2}\times0.3+(0.1)^{2}\times0.5+(1.1)^{2}\times0.2=0.81\times0.3 + 0.01\times0.5+1.21\times0.2$ $=0.243+0.005 + 0.242=0.49$

Step3: Calculate the standard deviation $\sigma$

$\sigma=\sqrt{Var(X)}=\sqrt{0.49}=0.70$

Answer:

$0.70$