Lat Soal Matstat
Lat Soal Matstat
Lat Soal Matstat
Contruct a relative frequency histogram for the voltage readings of the old process.
b.
Contruct a stem and leaf (diagram dahan daun) display for the voltage readings of
the old process. Which of the two graphs in parts a and b is more informative?
c.
Construct a relative frequency histogram for the voltage readings of the new
process
d.
Compare the two graphs in parts a and c. Does it appear that manufacturing
process can be established locally (i.e. is the new process as good as or better than
the old)
e.
Contruct a boxplot for each process. Give some comments to these graphs.
Latihan Soal
1
A survey of users of word processors showed that 10% were dissatisfied with the wordprocessing system they are currently using. Half of those who were dissatisfied had
purchased their systems from vendor A. If it is also known that 20% of all those
surveyed purchased their word-processing systems from vendor A. Given that a word
processor was purchased from vendor A, what is the probability that the user is
dissatisfied?
2.
A traffic engineer conducted a study of the urban mass transportation habits of a citys
workers. The study revealed the following : fifteen percent of the city workers regularly
drive their own car work. Of those who do drive their own car work, 80% would gladly
switch to public mass transportation if it were available. Forty percent of the city
workers live more than 3 miles from the center of the city.
Suppose that one city worker is chosen at random. Define the events A, B, and C as
follow :
A : {the person regularly drives his or her own car to work}
B : {the person would gladly switch to public mass transportation if it were available}
C : {The person lives within 3 miles of the center of the city}
a.
find p(A)
b.
find p(B|A)
c.
find p(C)
d.
Explain whether the pairs of events, A and B, A and C, B and C, are mutually
exclusive
3.
An assembler of computer terminals and modems uses parts from two sources.
Company A supplies 80 % of the parts and company B supplies the remaining 20 % of
the parts. From past experience, the assembler knows that 5% of the parts supplied by
company A rea defective and 3 % of the parts supplied by company B are defective. An
assembled modem selected at random is found to have a defective part. Which of the
two companies is more likely to have supplied the defective part?
4.
5.
f ( y)
3
(25 y 2 )
500
Find the mean and variance of the amount of time in seconds the train is late
4. Suppose we are counting events that occur according to a Poisson distribution, such as
the number of data-processing jobs submitted to a computer center. If it is known that
exactly one such event has occurred in a given interval of time, say (0,t), then the actual
time of occurrence is uniformly distributed over this interval. Suppose that during a
given 30-minute period, one data-processing job was submitted. Find the probability
that the job was submitted during the last 5 minutes of the 30-minute period.
5. Suppose that the fraction of defective modems shipped by a data-communications
vendor has an approximation beta distribution with =5 and =21.
a. find the mean and variance of the fraction of defective modems per shipment
b. What is the probability that a randomly selected shipment will contain at least 30 %
defectives?
Latihan Soal
3
c.
What is the probability that a randomly selected shipment will contain no more than
5 % defectives?
4. Teleconferences, electronic mail, and word processors are among the tools that can
reduce the length of business meetings. A recent survey indicated that the percentage
reduction y in time spent by business professionals in meetings due to automated office
equipment is approximately normally distributed with mean equel to 15% and standard
deviation equel to 4%.
a. what proportion of all business professionals with access to automated office
equipment have reduced their time in meetings by more than 22%
b. what proportion of all business professionals with access to automated office
equipment have reduced their time in meetings by 10 % or less?
From a group of three data-processing managers, two senior system analysts, and two
quality control engineers, three people are to randomly selected to form a committee
that will study the feasibility of adding computer graphics at a consulting firm. Let y 1
denote the number of data-processing managers and y 2 the number of senior systems
analysts selected for the committee.
a.
b.
Find E(y1-2y2)
c.
d.
e.
f.
g.
-1
-1
2/12
2/12
1
1/12 2/12 1/12
a. dapatkan fungsi peluang masing-masing Y1 serta Y2
b. apakah keduanya saling bebas ?
c.
Latihan Soal
4
3. The management of a bank must decide whether to install a commercial loan decisionsupport system (an on-line management information system) to aid its analysts in
making commercial loan decisions. Pat experience shows that y 1, the additional number
(per year) of correct loan decisions accepting good loan applications and rejecting
those that would eventually be defaulted attributable to the decision-support system,
and y2, the lifetime (in years) of the decision-support system, have the joint probability
distribution shown in the table :
Y1
0
Y2
10
20
30
40
50
60
70
80
90
0.005 0.005 0.010 0.075 0.100 0.075 0.050 0.030 0.030 0.025
0
0.002 0.005 0.005 0.020 0.030 0.015
5
a. find the marginal probability distribution of y1 and also y2.
Given the decision-support system is in its third year of operation, find the
probability that at least 40 additional correct loan decisions will be made
d. Find the expected lifetime of the decision-support system, i.e., find E(y 2)
e. Are y1 and y2 correlated? Are y1 and y2 independent?
f.
Each correct loan decision contributes approximately $25,000 to the banks profit.
Compute the mean and standars deviation of the additional profit attributable to the
decision-support system.
Latihan Soal
5