Page 83 - Applied statistics and probability for engineers

Section 2-8/Random Variables 61

(a) What is the probability that a part selected has a moderate (e) What is the probability that a sample conforms to the E 1 or
edge condition and a below-target bore depth? E 3 speciication?
(b) What is the probability that a part selected has a moderate (f) What is the probability that a sample conforms to the E 1 or
edge condition or a below-target bore depth? E 2 or E 3 speciication?
(c) What is the probability that a part selected does not have 2-206. Transactions to a computer database are either
a moderate edge condition or does not have a below-target new items or changes to previous items. The addition of an
bore depth? item can be completed in less than 100 milliseconds 90% of the
2-203. Computers in a shipment of 100 units contain a time, but only 20% of changes to a previous item can be com-
portable hard drive, solid-state memory, or both, according to pleted in less than this time. If 30% of transactions are changes,
the following table: what is the probability that a transaction can be completed in
less than 100 milliseconds?
Portable Hard Drive
2-207. A steel plate contains 20 bolts. Assume that 5 bolts
Solid-state memory Yes No are not torqued to the proper limit. 4 bolts are selected at ran-
Yes 15 80 dom, without replacement, to be checked for torque.
(a) What is the probability that all 4 of the selected bolts are
No 4 1
torqued to the proper limit?
Let A denote the event that a computer has a portable hard (b) What is the probability that at least 1 of the selected bolts is
drive, and let B denote the event that a computer has a solid- not torqued to the proper limit?
state memory. If one computer is selected randomly, compute 2-208. The following circuit operates if and only if there is a
(
(
(a) P A ( ) (b) P A∩ B) (c) P A∪ B) path of functional devices from left to right. Assume devices fail
(
(d) P A′ ′ B) (e) P A B| ( ) independently and that the probability of failure of each device
is as shown. What is the probability that the circuit operates?
2-204. The probability that a customer’s order is not
shipped on time is 0.05. A particular customer places three 0.01 0.01 0.1
orders, and the orders are placed far enough apart in time that
they can be considered to be independent events.
(a) What is the probability that all are shipped on time?
0.1 0.1
(b) What is the probability that exactly one is not shipped
on time?
2-209. The probability that concert tickets are available
(c) What is the probability that two or more orders are not
by telephone is 0.92. For the same event, the probability that
shipped on time?
tickets are available through a Web site is 0.95. Assume that
1 ,
2-205. Let E E 2 , and E 3 denote the samples that conform these two ways to buy tickets are independent. What is the
to a percentage of solids speciication, a molecular weight
probability that someone who tries to buy tickets through the
speciication, and a color speciication, respectively. A total of
Web and by phone will obtain tickets?
1 ,
240 samples are classiied by the E E 2 , and E 3 speciications, 2-210. The British government has stepped up its information
where yes indicates that the sample conforms.
campaign regarding foot-and-mouth disease by mailing bro-
E yes chures to farmers around the country. It is estimated that 99%
3
of Scottish farmers who receive the brochure possess enough
E
2 information to deal with an outbreak of the disease, but only
Yes No Total 90% of those without the brochure can deal with an outbreak.
E Yes 200 1 201 After the irst three months of mailing, 95% of the farmers in
1
No 5 4 9 Scotland had received the informative brochure. Compute the
probability that a randomly selected farmer will have enough
Total 205 5 210
information to deal effectively with an outbreak of the disease.
E no 2-211. In an automated illing operation, the probability of
3
an incorrect ill when the process is operated at a low speed is
E
2 0.001. When the process is operated at a high speed, the probabil-
Yes No Total ity of an incorrect ill is 0.01. Assume that 30% of the containers
E Yes 20 4 24 are illed when the process is operated at a high speed and the
1
No 6 0 6 remainder are illed when the process is operated at a low speed.
Total 26 4 30 (a) What is the probability of an incorrectly illed container?
(b) If an incorrectly illed container is found, what is the prob-
1 ,
(a) Are E E 2 , and E 3 mutually exclusive events?
1 ′ , and E 3 ′ mutually exclusive events?
(b) Are E E 2 ′, ability that it was illed during the high-speed operation?
(c) What is P(E 1 ′ or E 2 ′ or E 3 ′)? 2-212. An encryption-decryption system consists of three
(d) What is the probability that a sample conforms to all three elements: encode, transmit, and decode. A faulty encode occurs
speciications? in 0.5% of the messages processed, transmission errors occur