Page 82 - Applied statistics and probability for engineers

60 Chapter 2/Probability

Let A denote the event that a batch is formed from two dif- of time reading and writing, and the probability that the useful
ferent lots, and let B denote the event that a lot requires addi- life exceeds ive years is 0.995. Now, 25% of the products from
tional processing. Determine the following probabilities: a manufacturer are used for backup and 75% of the products are
(
(a) P A ( ) (b) P A′ ( ) (c) P B A| ( ) (d) P B A| ′) used for main storage.
(
(
B′
(e) P A∩ B) (f) P A∩ ) (g) P B ( ) Let A denote the event that a laser’s useful life exceeds ive
years, and let B denote the event that a laser is in a product that
2-194. Incoming calls to a customer service center are
classiied as complaints (75% of calls) or requests for informa- is used for backup.
(b) P A B)
| (
tion (25% of calls). Of the complaints, 40% deal with computer Use a tree diagram to determine the following:
| (
(c) P A B′)
equipment that does not respond and 57% deal with incomplete (a) P B ( ) B) (e) P A∩ ) P A ( )
(
(
software installation; in the remaining 3% of complaints, the (d) P A∩ B′ (f)
user has improperly followed the installation instructions. The (g) What is the probability that the useful life of a laser exceeds
requests for information are evenly divided on technical ques- ive years?
tions (50%) and requests to purchase more products (50%). (h) What is the probability that a laser that failed before ive
(a) What is the probability that an incoming call to the cus- years came from a product used for backup?
tomer service center will be from a customer who has not 2-199. Energy released from cells breaks the molecular bond
followed installation instructions properly? and converts ATP (adenosine triphosphate) into ADP (adeno-
(b) Find the probability that an incoming call is a request for sine diphosphate). Storage of ATP in muscle cells (even for an
purchasing more products. athlete) can sustain maximal muscle power only for less than
2-195. A congested computer network has a 0.002 ive seconds (a short dash). Three systems are used to replen-
probability of losing a data packet, and packet losses are ish ATP—phosphagen system, glycogen-lactic acid system
independent events. A lost packet must be resent. (anaerobic), and aerobic respiration—but the irst is useful only
(a) What is the probability that an e-mail message with 100 for less than 10 seconds, and even the second system provides
packets will need to be resent? less than two minutes of ATP. An endurance athlete needs to
(b) What is the probability that an e-mail message with 3 packets perform below the anaerobic threshold to sustain energy for
will need exactly 1 to be resent? extended periods. A sample of 100 individuals is described by
(c) If 10 e-mail messages are sent, each with 100 packets, what the energy system used in exercise at different intensity levels.
is the probability that at least 1 message will need some Primarily Aerobic
packets to be resent?
2-196. Samples of a cast aluminum part are classiied on the Period Yes No
basis of surface inish (in microinches) and length measurements. 1 50 7
The results of 100 parts are summarized as follows:
2 13 30
Length Let A denote the event that an individual is in period 2, and let
Excellent Good B denote the event that the energy is primarily aerobic. Deter-
Surface Excellent 80 2 mine the number of individuals in
(a) A′ ′ B (b) B′ (c) A∪ B
Finish Good 10 8
Let A denote the event that a sample has excellent surface 2-200. A sample preparation for a chemical measurement is
inish, and let B denote the event that a sample has excellent completed correctly by 25% of the lab technicians, completed with
length. Are events A and B independent? a minor error by 70%, and completed with a major error by 5%.
2-197. An optical storage device uses an error (a) If a technician is selected randomly to complete the preparation,
recovery procedure that requires an immediate satisfactory read- what is the probability that it is completed without error?
back of any written data. If the readback is not successful after (b) What is the probability that it is completed with either a
three writing operations, that sector of the disk is eliminated as minor or a major error?
unacceptable for data storage. On an acceptable portion of the 2-201. In circuit testing of printed circuit boards, each board either
disk, the probability of a satisfactory readback is 0.98. Assume fails or does not fail the test. A board that fails the test is then checked
the readbacks are independent. What is the probability that an further to determine which one of ive defect types is the primary
acceptable portion of the disk is eliminated as unacceptable for failure mode. Represent the sample space for this experiment.
data storage? 2-202. The data from 200 machined parts are summarized as
2-198. Semiconductor lasers used in optical storage products follows:
require higher power levels for write operations than for read
operations. High-power-level operations lower the useful life Depth of Bore
of the laser. Edge Condition Above Target Below Target
Lasers in products used for backup of higher-speed Coarse 15 10
magnetic disks primarily write, and the probability that the use-
Moderate 25 20
ful life exceeds ive years is 0.95. Lasers that are in products that
are used for main storage spend approximately an equal amount Smooth 50 80