Answer:
18.33
Step-by-step explanation:
Given the probability distribution below:
[tex]\left|\begin{array}{c|cccc}$Daily number of customers& 20 & 40 &60 & 80 \\$Probability&0.2&0.3&0.4 &0.1\end{array}\right|[/tex]
We are required to determine the standard deviation of the number of daily customers.
[tex]\text{Standard Deviation}=\sqrt{\sum (x-E(x))^2 \cdot P(x)}[/tex]
Mean, E(x)=20*0.2+40*0.3+60*0.4+80*0.1=48
[tex]\left|\begin{array}{c|c|c|c|c}x&x-E(x)&(x-E(x))^2&P(x)&(x-E(x))^2 \cdot P(x)\\20&-28&784&0.2&156.8\\40&-8&64&0.3&19.2\\60&12&144&0.4&57.6\\80&32&1024&0.1&102.4\\Total&&&&336\end{array}\right][/tex]
Standard Deviation[tex]=\sqrt{336}=18.33[/tex]
