Answer:
Step-by-step explanation:
The data:
[tex]\begin{matrix}i= & 1 & 2 & 3 & 4 & 5 & 6\\X= & 0 & 1 & 2 & 3 & 4 & 5\\P= & 0.6 & 0.2 & 0.12 & 0.4 & 0.4 & 0\end{matrix}[/tex]
whereby [tex]i, X, P[/tex] correspondingly represent the index number, the number of days absent and the corresponding probability.
Firstly we calculate the expected number of days absent using the following formula:
[tex]E(X)=\sum_{i=1}^{6}X_i P_i = 0.72[/tex]
Subsequently, we calculate the standard deviation using the following formula:
[tex]\\\sigma =\sqrt{\sum_{i=1}^{6}P_i\times[X_i-E(X)]^2}=1.0778[/tex]
For the detailed calculation, please see the attached Excel file.
