Question

$P(x=4)$= _______

Short answer

The probability of $P(x=4)=0.10$.

Step-by-step solution

Given Information

The probability of $P(X=4)$from the given table.

A corporation want to assess its attrition rate, or the length of time that new personnel stay with the organization. They've developed the following probability distribution over time.

Concept Used

Let us define $X$ be the number of years a new hire will stay with the company and $P\left(X\right)$the probability that a new hire will stay with the company $X$years.

Only when, according to discrete distribution features, is $P\left(X\right)$ said to be the probability mass function of a $X$ discrete variable.

i. $P\left(X\right)$$\ge$0 for all$X$
ii.localid="1648447521559" $\sum P\left(X\right)=1$

Calculation

We may calculate the probability using condition (ii)$P(X=4)$as:

localid="1649438056252" $$\begin{gathered} \sum P\left(X\right)=0.12+0.18+0.30+0.15+P\left(X_4\right)+0.10+0.05=1 \\ P\left(X_4\right)=1-0.90=0.10 \end{gathered}$$

Conclusion:

As a result, the probability is:

$P(x=4)=0.10$