Question

What does the column “$P\left(x\right)$” sum to?

Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to

sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established

a probability distribution.

Short answer

The sum of the columns$P\left(X\right)$ is $1$.

Step-by-step solution

Given Information

The column $P\left(X\right)$total from the table is used. A business needs to assess its attrition rate, or how long new employees stay with the organization.

They've developed the following probability distribution over time.

 Concept Used

Let's define$X$the number of years a new hire will stay with the company $P\left(X\right)$and the probability of staying with the company for$X$ years.

The probability mass function of a discrete variable is $P\left(X\right)$and the probability mass function of a discrete variable $X$only when,

i. $P\left(X\right)\ge 0$for all $X$

ii.$\sum P\left(X\right)=1$

Calculation

The column sum can be calculated using condition (ii) as:

$\sum P\left(X\right)=0.12+0.18+0.30+0.15+0.10+0.10+0.05=1$

Conclusion:

As a result, the sum of the columns $P\left(X\right)$is $1$.