Performance-based logistics. Refer to the Journal of Business Logistics (Vol. 36, 2015) study of performance-based logistics (PBL) strategies, Exercise 1.15 (p. 49). Recall that the study was based on the opinions of a sample of 17 upper-level employees of the U.S. Department of Defense and its suppliers. The current position (e.g., vice president, manager), type of organization (commercial or government), and years of experience for each team member interviewed are listed below. Suppose we randomly select one of these interviewees for more in-depth questioning on PBL strategies.

a. What is the probability that the interviewee works for a government organization?

b. What is the probability that the interviewee has at least 20 years of experience?

Interviewee	Position	Organization	Experience (years)
1	Vice president	Commercial	30
2	Postproduction	Government	15
3	Analyst	Commercial	10
4	Senior manager (mgr.)	Government	30
5	Support chief	Government	30
6	Specialist	Government	25
7	Senior analyst	Commercial	9
8	Division chief	Government	6
9	Item mgr.	Government	3
10	Senior mgr.	Government	20
11	MRO mgr.	Government	25
12	Logistics mgr.	Government	30
13	MRO mgr.	Commercial	10
14	MRO mgr.	Commercial	5
15	MRO mgr.	Commercial	10
16	Specialist	Government	20
17	Chief	Government	25

Step by step solution

01

Step-by-Step SolutionStep 1: Introduction

Probability is a measure of the possibility that an event will occur in a Random Experiment. The probability formula is used to calculate the likelihood of an event occurring. The following is the formula for calculating the probability of an occurrence:

$\mathbf{Probability}\mathbf{=}\frac{\mathbf{Favourable}\mathbf{}\mathbf{outcome}}{\mathbf{Total}\mathbf{}\mathbf{}\mathbf{outcome}}$

02

Find the probability of government organization

$\begin{array}{l}\mathbf{Total}\mathbf{}\mathbf{of}\mathbf{}\mathbf{government}\mathbf{}\mathbf{organization}\mathbf{=}\mathbf{15}\mathbf{+}\mathbf{30}\mathbf{+}\mathbf{30}\mathbf{+}\mathbf{25}\mathbf{+}\mathbf{6}\mathbf{+}\mathbf{3}\mathbf{+}\mathbf{20}\mathbf{+}\mathbf{25}\mathbf{+}\mathbf{30}\mathbf{+}\mathbf{20}\mathbf{+}\mathbf{25}\\ \mathbf{=}\mathbf{229}\end{array}$

role="math" localid="1653480317687" $\begin{array}{c}\mathbf{P}\mathbf{(}\mathbf{Government}\mathbf{}\mathbf{organization}\mathbf{)}\mathbf{=}\frac{\mathbf{229}}{\mathbf{303}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{75}\end{array}$

Hence, the required probability is 0.75.

03

Find the probability of at least 20 years of experience

$\begin{array}{l}\mathbf{Total}\mathbf{}\mathbf{of}\mathbf{}\mathbf{atleast}\mathbf{}\mathbf{20}\mathbf{years}\mathbf{}\mathbf{experience}\mathbf{=}\mathbf{15}\mathbf{+}\mathbf{10}\mathbf{+}\mathbf{9}\mathbf{+}\mathbf{6}\mathbf{+}\mathbf{3}\mathbf{+}\mathbf{20}\mathbf{+}\mathbf{10}\mathbf{+}\mathbf{5}\mathbf{+}\mathbf{10}\mathbf{+}\mathbf{20}\\ \mathbf{=}\mathbf{108}\end{array}$

role="math" localid="1653480437013" $\begin{array}{c}\mathbf{P}\mathbf{(}\mathbf{atleast}\mathbf{}\mathbf{20}\mathbf{years}\mathbf{)}\mathbf{=}\frac{\mathbf{108}}{\mathbf{303}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{36}\end{array}$

Hence, the required probability is 0.36.

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