Page 53 - Applied Statistics And Probability For Engineers

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36 CHAPTER 2 PROBABILITY

probability is the sum of any collection of mutually exclusive events with union equal to the
same range for X. One example is

P16.5 X 7.82 P16.5 X 7.02 P17.0 X 7.52 P17.5 X 7.82

Another example is

P16.5 X 7.82 P16.5 X 6.62 P16.6 X 7.12
P17.1 X 7.42 P17.4 X 7.82

The best choice depends on the particular probabilities available.

EXERCISES FOR SECTION 2-3

2-49. If P 1A2 0.3 , P 1B2 0.2, and P 1A ¨ B2 0.1, (a) If a shaft is selected at random, what is the probability that
determine the following probabilities: the shaft conforms to surface finish requirements?
(a) P1A¿2 (b) P1A ´ B2 (b) What is the probability that the selected shaft conforms
(c) P1A¿¨ B2 (d) P1A ¨ B¿2 to surface finish requirements or to roundness require-
(e) P31A ´ B2¿4 (f) P1A¿´ B2 ments?
2-50. If A, B, and C are mutually exclusive events with (c) What is the probability that the selected shaft either con-
P 1A2 0.2, P 1B2 0.3, and P 1C2 0.4, determine the fol- forms to surface finish requirements or does not conform
lowing probabilities: to roundness requirements?
(a) P1A ´ B ´ C2 (b) P1A ¨ B ¨ C2 (d) What is the probability that the selected shaft conforms to
(c) P1A ¨ B2 (d) P31A ´ B2 ¨ C4 both surface finish and roundness requirements?
(e) P1A¿¨ B¿¨ C¿2 2-54. Cooking oil is produced in two main varieties: mono-
2-51. If A, B, and C are mutually exclusive events, is it pos- and polyunsaturated. Two common sources of cooking oil are
sible for P(A) 0.3, P(B) 0.4, and P(C) 0.5? Why or corn and canola. The following table shows the number of
why not? bottles of these oils at a supermarket:
2-52. Disks of polycarbonate plastic from a supplier are an- type of oil
alyzed for scratch and shock resistance. The results from 100 canola corn
disks are summarized as follows:
type of mono 7 13
shock resistance unsaturation poly 93 77
high low (a) If a bottle of oil is selected at random, what is the proba-
scratch high 70 9 bility that it belongs to the polyunsaturated category?
resistance low 16 5 (b) What is the probability that the chosen bottle is monoun-
saturated canola oil?
(a) If a disk is selected at random, what is the probability that
its scratch resistance is high and its shock resistance is 2-55. A manufacturer of front lights for automobiles tests
high? lamps under a high humidity, high temperature environment
(b) If a disk is selected at random, what is the probability using intensity and useful life as the responses of interest. The
that its scratch resistance is high or its shock resistance following table shows the performance of 130 lamps:
is high? useful life
(c) Consider the event that a disk has high scratch resistance satisfactory unsatisfactory
and the event that a disk has high shock resistance. Are intensity satisfactory 117 3
these two events mutually exclusive?
unsatisfactory 8 2
2-53. The analysis of shafts for a compressor is summarized
by conformance to specifications. (a) Find the probability that a randomly selected lamp will
yield unsatisfactory results under any criteria.
roundness conforms
(b) The customers for these lamps demand 95% satisfactory
yes no results. Can the lamp manufacturer meet this demand?
surface finish yes 345 5 2-56. The shafts in Exercise 2-53 are further classified in terms
conforms no 12 8 of the machine tool that was used for manufacturing the shaft.