Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

19.5 Normal Distribution 643

19.5 Normal Distribution

In Section 19.1, we explained what we mean by a statistical experiment and outcome. Recall

that the result of an experiment is called an outcome. In an engineering situation, we often per-

form experiments that could have many outcomes. To organize the outcomes of an experiment,

it is customary to make use of probability distributions. A probability distribution shows the

probability values for the occurrence of the outcomes of an experiment. To better understand

the concept of probability distribution, let’s turn our attention to Example 19.2. If we were to

consider the chemistry test as an experiment with outcomes represented by student scores, then

we can calculate a probability value for each range of scores by dividing each frequency by

26 (the total number of scores). The probability distribution for Example 19.2 is given in

Table 19.9. From examining Table 19.9, you should note that the sum of probabilities is 1,

which is true for any probability distribution. The plot of the probability distribution for

Example 19.2 is shown in Figure 19.4. Moreover, if this was a typical chemistry test with typical

TABLE 19.9 Probability Distribution for Example 19.2

Range Frequency Probability

50 –59 3 0.115

60 – 69 5 0.192

70 –79 9 0.346

80 – 89 6 0.231

90 – 99 3 0.115

gp 1

3

26

6

26

9

26

5

26

3

26

Probability

0.400

0.350

0.300

0.250

0.200

0.150

0.100

0.050

0.000

50–59 60–69 70–79 80–89 90–99

Scores

■Figure 19.4

Plot of probability distribution

for Example 19.2.

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