Page 72 - Applied Statistics And Probability For Engineers

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2-8 RANDOM VARIABLES 55

(d) The outside diameter of a machined shaft. (a) What is the probability that all are shipped on time?
(e) The number of cracks exceeding one-half inch in 10 miles (b) What is the probability that exactly one is not shipped on
of an interstate highway. time?
(f) The weight of an injection-molded plastic part. (c) What is the probability that two or more orders are not
(g) The number of molecules in a sample of gas. shipped on time?
(h) The concentration of output from a reactor. 2-105. Let E 1 , E 2 , and E 3 denote the samples that conform
(i) The current in an electronic circuit. to a percentage of solids specification, a molecular weight
specification, and a color specification, respectively. A total of
Supplemental Exercises 240 samples are classified by the E 1 , E 2 , and E 3 specifications,
where yes indicates that the sample conforms.
2-101. In circuit testing of printed circuit boards, each
board either fails or does not fail the test. A board that fails the
E 3 yes
test is then checked further to determine which one of five de-
fect types is the primary failure mode. Represent the sample E 2
space for this experiment. yes no Total
2-102. The data from 200 machined parts are summarized E 1 yes 200 1 201
as follows: no 5 4 9
Total 205 5 210
depth of bore
E 3 no
above below
edge condition target target E 2
yes no
coarse 15 10
yes 20 4 24
moderate 25 20
E 1
no 6 0 6
smooth 50 80
Total 26 4 30
(a) What is the probability that a part selected has a moderate
edge condition and a below-target bore depth?
(b) What is the probability that a part selected has a moderate (a) Are E 1 , E 2 , and E 3 mutually exclusive events?
edge condition or a below-target bore depth? (b) Are E 1 , E 2 , and E 3 mutually exclusive events?
(c) What is the probability that a part selected does not have a (c) What is P(E 1 or E 2 or E 3 )?
moderate edge condition or does not have a below-target (d) What is the probability that a sample conforms to all three
bore depth? specifications?
(d) Construct a Venn diagram representation of the events in (e) What is the probability that a sample conforms to the E 1 or
this sample space. E 3 specification?
(f) What is the probability that a sample conforms to the E 1 or
2-103. Computers in a shipment of 100 units contain a E 2 or E 3 specification?
portable hard drive, CD RW drive, or both according to the
following table: 2-106. Transactions to a computer database are either new
items or changes to previous items. The addition of an item can
portable hard drive be completed less than 100 milliseconds 90% of the time, but
yes no only 20% of changes to a previous item can be completed in
CD RW less than this time. If 30% of transactions are changes, what is
yes 15 80 the probability that a transaction can be completed in less than
no 4 1 100 milliseconds?
Let A denote the events that a computer has a portable hard 2-107. A steel plate contains 20 bolts. Assume that 5 bolts
drive and let B denote the event that a computer has a CD RW are not torqued to the proper limit. Four bolts are selected at
drive. If one computer is selected randomly, compute random, without replacement, to be checked for torque.
(a) What is the probability that all four of the selected bolts
(a) P1A2 (b) P1A ¨ B2
are torqued to the proper limit?
(c) P1A ´ B2 (d) P1A¿¨ B2
(b) What is the probability that at least one of the selected
(e) P1A ƒ B2
bolts is not torqued to the proper limit?
2-104. The probability that a customer’s order is not
2-108. The following circuit operates if and only if there is
shipped on time is 0.05. A particular customer places three
a path of functional devices from left to right. Assume devices
orders, and the orders are placed far enough apart in time that
fail independently and that the probability of failure of each
they can be considered to be independent events.