EX 3.15 days of sick leave

Let $X=$ the number of days of sick leave taken by a randomly selected employee of a large company during a particular year. If the maximum number of allowable sick days per year is 14, possible values of $X$ are $0,1,\dots ,14$ . With

• $F\left(0\right)=.58$
• $F\left(1\right)=.72$
• $F\left(2\right)=.76$
• $F\left(3\right)=.81$
• $F\left(4\right)=.88$
• $F\left(5\right)=.94$ , We have

$$\begin{array}{rl}P(2\le X\le 5)& =P(X=2,3,4\text{, or }5)\\ & =F(5)-F(1)\\ & =0.22\end{array}$$

and $P\left(X=3\right)=F\left(3\right)-F\left(2\right)=.05$