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

648 Chapter 19 Probability and Statistics in Engineering

Example 19.6 For Example 19.4, calculate the mean and standard deviation, and determine the probability

that it will take a person between 7 and 11 minutes to assemble the computer parts. Refer to

Table 19.12 when following solution steps.

z  1.00z  1.00

A  0.3413  0.3413 ≈ 0.68 A  0.4772  0.4772 ≈ 0.95

z  2.00 z  2.00

■Figure 19.7 The area under a normal curve for Example 19.5.

mean) each represent 0.4772% of the total area under the normal curve. Then, as shown in

Figure 19.7, 95% of the data fall in the interval of  2 sto 2s. In the same way, we can show that

99.7% (forz3 thenA0.4987 andz3 thenA0.4987) or almost all of the data

points lie between  3 sto 3s.

TABLE 19.12 Data for Example 19.6

Time

(minutes) Frequency

xfxf

5525 4.22 89.04

6848 3.22 82.95

71 1 7 7 2.22 54.21

8 15 120 1.22 22.33

9 17 153 0.22 0.82

10 14 140 0.78 8.52

11 13 143 1.78 41.19

12 8 96 2.78 61.83

13 6 78 3.78 85.73

14 3 42 4.78 168.55

gxf 922 g 1 xx 22 f 515.16

1 xx 2

2

xx f

s

B

g 1 xx 2

2

f

n 1



B

515.16

99

2.28 minutes

x

g x f

n



922

100

9.22 minutes

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