Mathematics: A small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data. Sales Quality Operations Total Traditional 16 10 8 34 Online 35 23 44 102 Total 51 33 52 136 Required: a. What is the probability that an employee chose online training? b. What is the probability

43.3Step-by-step explanation:500 - 66 - 4 - 300 = 130 apples130/343.3...

A small manufacturing company recently instituted

dajiaglosson

12.08.2021

(a) $P(Online\ Training) = 0.750$

(b) Pr = 0.169 --- Quality Division and Online Training

Step-by-step explanation:

Given

The two-way table

Solving (a): P(Online Training)

The total employee is:

Total = 136

The employees for online training is:

$Online\ Training = 102$

So, the probability is:

$P(Online\ Training) = \frac{102}{136}$

$P(Online\ Training) = 0.750$

Solving (b): P(Quality Division and Online Training)

The number of employees that choose quality Division and online training is 23

So, the probability is:

$Pr = \frac{23}{136}$

Pr = 0.169

Solving (c): P(Online Training | Sales Division)

This is calculated as:

Let:

$A \to$ Online training

$B \to$ Sales division

So, we have:

$P(A\ |\ B) = \frac{n(A\ n\ B)}{n(B)}$

From the table:

$n(A\ n\ B) =35$

n(B) = 16 + 35 = 51

So, the probability is:

$P(A\ |\ B) = \frac{35}{51}$

$P(A\ |\ B) = 0.686$

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