5.1 Materi Statistika Deskriptif
A harris Corporational/University of Florida study was undertaken to determine whether a manufacturing
process performed at a remote location can be established locally. Test devices (pilots) were set up at both the
old and new locations and voltage readings on the process were obtained. A “good process” was considered to
be one with voltage readings of at least 9.2 volt (with larger readings being better than samller readings). The
table contains voltage readings for 30 production runs at each location.
a.
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.
5.2 Pengantar Hitung Peluang
1.
A survey of users of word processors showed that 10% were dissatisfied with the word-processing 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 city’s 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
Latihan Soal
5-1
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.
A quality control engineer samples five from a large lot of manufactured firing pins and checks for defect.
Unknown to the inspector, three of the five sampled firing pins are defective. The engineer will test the
five pins in randomly selected order until a defective is observed (in which case the entire lot will be
rejected). Let y be the number of firing pins the quality control engineer must test. Find the probability
distribution of y.
5.
A random sample of 25 computer programmers was selected to compare two full-screen-edit intelligent
terminals, one manufactured by vendor A and the other by vendor B. After working with the two types of
terminals, each programmer was asked to choose the terminal that he or she preferred. Let y be the
number of sampled programmers who prefer the terminal manufactured by vendor A.
a.
b.
c.
is y a binomial random variable?
If the two terminals are, in fact, identical, then p=0.5. Find p(y19)
If observe y=19, what would you infer about the true value of p?
5.3 Peubah Acak Kontinyu
3.
The amount of time y (in minutes) that a commuter train is late is a continuous random variable with
probability density :
f ( y) 
3
(25  y 2 )
500
untuk –5<y<5 (a negative value of y means that the train is early)
a.
Find the mean and variance of the amount of time in minutes the train is late.
b.
Find the mean and variance of the amount of time in hours the train is late
c.
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.
4.
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?
c.
What is the probability that a randomly selected shipment will contain no more than 5 % defectives?
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?
Latihan Soal
5-2
5.4 Peubah Acak Ganda
1.
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
y2 the number of senior systems analysts selected for the committee.
a.
Determine whether y1 and y2 are independent
b.
Find E(y1-2y2)
c.
Find the covariance of the random variable y 1 and y2.
d.
Find the varianve of y1 and also the variance of y2
e.
Find the correlation of the random variable y 1 and y2
f.
Find the covariance matrix of the random variable y1 and y2
g.
Find the correlation matrix of the random variable y 1 and y2
2. Berikut adalah fungsi peluang gabungan peubah acak y1 dengan y2 :
Y1
3.
Y2
-1
0
1
-1
1/12
2/12
1/12
0
2/12
0
2/12
a.
1
1/12 2/12 1/12
dapatkan fungsi peluang masing-masing Y1 serta Y2
b.
apakah keduanya saling bebas ?
c.
hitung matriks kovariance dua peubah acak tersebut
The management of a bank must decide whether to install a commercial loan decision-support system (an
on-line management information system) to aid its analysts in making commercial loan decisions. Pat
experience shows that y1, 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
Y2
0
10
20
30
40
50
60
70
80
90
1
0.001
0.002
0.002
0.025
0.040
0.025
0.005
0.005
0
0
2
0.005
0.005
0.010
0.075
0.100
0.075
0.050
0.030
0.030
0.025
3
0
0
0
0.025
0.050
0.080
0.050
0.080
0.040
0.030
4
0
0.001
0.002
0.005
0.010
0.025
0.010
0.003
0.001
0.001
0
0.002 0.005 0.005 0.020 0.030
5
find the marginal probability distribution of y1 and also y2.
0.015
0
0
0
a.
b.
Find the probability distribution p1(y1|y2)
c.
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(y2)
e.
f.
Are y1 and y2 correlated? Are y1 and y2 independent?
Each correct loan decision contributes approximately $25,000 to the bank’s profit. Compute the
mean and standars deviation of the additional profit attributable to the decision-support system.
Latihan Soal
5-3
Latihan Soal
5-4