Question

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. Number of Days Absent Probability 0 0.60 1 0.20 2 0.12 3 0.04 4 0.04 5 0.00 What is the standard deviation of the number of days absent?

Answer 1

Answer:

Step-by-step explanation:

The data:

$\begin{matrix}i= & 1 & 2 & 3 & 4 & 5 & 6\\X= & 0 & 1 & 2 & 3 & 4 & 5\\P= & 0.6 & 0.2 & 0.12 & 0.4 & 0.4 & 0\end{matrix}$

whereby $i, X, P$ 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:

$E(X)=\sum_{i=1}^{6}X_i P_i = 0.72$

Subsequently, we calculate the standard deviation using the following formula:

$\\\sigma =\sqrt{\sum_{i=1}^{6}P_i\times[X_i-E(X)]^2}=1.0778$

For the detailed calculation, please see the attached Excel file.

Download xlsx