Mathematics, 13.07.2021 16:00 slycooper99

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 that an employee is in the Quality division and chose online training?
c. What is the probability that an employee chose online training given that he/she is in the Sales division?

Answers: 3

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Answer from: drashanhparekh123

(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:

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

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

Answer from: Quest

answer: the proof is mentioned below.

step-by-step explanation:

since, given: lines bc = ef

prove: lines ac > ef

statements reason

1. bc=ef 1. given

2. ac= ab+bc 2. because b is the point between the

line segment ac

3. ac > bc 3. because if a line segment is equal to

the sum of two line segments then it is

always greater then each of these

individual line segments

4. ac > ef 4. by equality property.

Answer from: Quest

Ithink the answer may be -7 by when dividing both sides by -3

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