the same conditions, with a certain outcome occurringmtimes, the relative frequency of
the outcome is given bym/n. Asngets larger, then theprobability pof a specific outcome
is given bypm/n.Example 19.1 Each question on a multiple-choice exam has five answers listed. Knowing that only one of the
answers is correct, if you are unprepared for the exam, what is the probability that you pick the
correct answer?For those of you who follow sports, you may have noticed that sometimes the probability
of a certain outcome is expressed in terms of odds. For example, the odds in favor of your team
winning may be given as 1 to 2. What does “odds in favor of an event” mean? The odds in favor
of an event occurring is defined by probability (occuring)/probability (not occuring). Therefore,
if the probability of your team winning is given by 0.33, then the odds in favor of your team
winning is given by 0.33/0.661/2 or 1 to 2. On the other hand, if the odds are expressed
asxtoy, then the probability of a specific outcome is calculated fromx/(xy). For this
example, as expected,p1/(12) 0.33.As you take advanced classes in engineering, you will learn more about the mathematical mod-
els that provide probabilities of certain outcomes. Our intent here is to make you aware of the impor-
tance of probability and statistics in engineering, not to provide detailed coverage of these topics.19.2 Statistics–Basic Ideas
Statistics is that area of science that deals with collection, organization, analysis, and interpreta-
tion of data. Statistics also deals with methods and techniques that can be used to draw conclu-
sions about the characteristics of something with a large number of data points — commonly
called apopulation— using a smaller portion of the entire data. For example, using statistics, we
can predict the outcome of an election in a state, say with two million registered voters, by gath-
ering information only from 1000 people about how they are planning to vote. As this example
demonstrates, it is neither feasible nor practical to contact two million people to find out how
they are planning to vote. However, the sample selected from a population must represent the
characteristics of the population. It is important to note that, in statistics, population does not
refer necessarily to people but to all of the data that pertain to a situation or a problem. For
example, if a company is producing 15,000 screws a day and they want to examine the quality
of the manufactured screws, they may select only 500 screws randomly for a quality test. In this
example, 15,000 screws is the population, and the 500 selected screws represents the sample.
Statistical models are becoming common tools in the hands of practicing engineers to
address quality control and reliability issues and to perform failure analyses. At this stage of
your education, it is important to realize that, in order to use statistical models, you need first
to completely understand the underlying concepts. The next sections are devoted to some of
these important concepts.p
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19.2 Statistics —Basic Ideas 635
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