Applied Statistics and Probability for Engineers, 6th Edition
Authors: Douglas C. Montgomery, George C. Runger
ISBN-13: 978-1118539712
See our solution for Question 14E from Chapter 2 from Applied Statistics and Probability for Engineers by Montgomery.
Problem 14E
Chapter:
Problem:
Step-by-Step Solution
Given Information
An order for an automobile can specify either an automatic or a standard transmission, either with or without air conditioning, and with any one of the four colors red, blue, black, or white.
Step-1: Possible Combinations
The Automobile can be either Automatic or Standard Transmission
Following combination can be formed \[\left\{ {{\rm{Automobile}}} \right\} \to \left\{ \begin{array}{l}{\rm{Standard}}\,\,{\rm{(S)}}\\{\rm{Automatic}}\,\,{\rm{(A)}}\end{array} \right\} \to \left\{ \begin{array}{l}{\rm{With}}\,\,{\rm{Air}}\,{\rm{Conditioning}}\,\,{\rm{(AC)}}\\{\rm{Without}}\,\,{\rm{Air}}\,{\rm{Conditioning}}\,{\rm{(N)}}\end{array} \right\} \to \left\{ \begin{array}{l}{\rm{Red}}\,\,{\rm{(Rd)}}\\{\rm{Blue}}\,{\rm{(Bl)}}\\{\rm{Black}}\,{\rm{(Bk)}}\\{\rm{White}}\,{\rm{(Wh)}}\end{array} \right\}\]
Step-1: The Sample Space
Therefore, the sample space is \[\boxed{S = \left\{ \begin{array}{l}{\rm{S - AC - Rd,S - AC - Bl,S - AC - Bk,S - AC - Wh,}}\\{\rm{S - N - Rd,S - N - Bl,S - N - Bk,S - N - Wh,}}\\{\rm{A - AC - Rd,A - AC - Bl,A - AC - Bk,A - AC - Wh,}}\\{\rm{A - N - Rd,A - N - Bl,A - N - Bk,A - N - Wh,}}\end{array} \right\}}\]
An order for an automobile can specify either an automatic or a standard transmission, either with or without air conditioning, and with any one of the four colors red, blue, black, or white.
Step-1: Possible Combinations
The Automobile can be either Automatic or Standard Transmission
Following combination can be formed \[\left\{ {{\rm{Automobile}}} \right\} \to \left\{ \begin{array}{l}{\rm{Standard}}\,\,{\rm{(S)}}\\{\rm{Automatic}}\,\,{\rm{(A)}}\end{array} \right\} \to \left\{ \begin{array}{l}{\rm{With}}\,\,{\rm{Air}}\,{\rm{Conditioning}}\,\,{\rm{(AC)}}\\{\rm{Without}}\,\,{\rm{Air}}\,{\rm{Conditioning}}\,{\rm{(N)}}\end{array} \right\} \to \left\{ \begin{array}{l}{\rm{Red}}\,\,{\rm{(Rd)}}\\{\rm{Blue}}\,{\rm{(Bl)}}\\{\rm{Black}}\,{\rm{(Bk)}}\\{\rm{White}}\,{\rm{(Wh)}}\end{array} \right\}\]
Step-1: The Sample Space
Therefore, the sample space is \[\boxed{S = \left\{ \begin{array}{l}{\rm{S - AC - Rd,S - AC - Bl,S - AC - Bk,S - AC - Wh,}}\\{\rm{S - N - Rd,S - N - Bl,S - N - Bk,S - N - Wh,}}\\{\rm{A - AC - Rd,A - AC - Bl,A - AC - Bk,A - AC - Wh,}}\\{\rm{A - N - Rd,A - N - Bl,A - N - Bk,A - N - Wh,}}\end{array} \right\}}\]