BUS121
(Statistics for Business)
UNIVERSITY OF WOLLONGONG
FACULTY OF BUSINESS AND LAW
Tutorial 2 Questions
Chapter 4
Note: Questions with * are covered in the tutorial.
*1) Use the values in the contingency table to solve the following equations:
Variable 1
Variable 2
E
F
Total
A
85
75
160
B
40
55
95
C
40
85
125
D
95
25
120
Total
260
240
500
a. P(F) = 240/500
b. P(B  C) = 0/500 ,
can’t happen coz
mutually exclusive
c. P(B  F) = 280/500 ?
d. P(F | B) =
(55/500)/(95/500) =
11/19
e. P(D  F) = 25/500
f. P(A | B) =
(255/500)/(95/500) =
51/19 ? or 0?
mutually exclusive
g. P(B | F) =
h. P(B) = 95/500
(55/500)/(240/500) =
11/48
i. P(A  B) =
(160/500) + (95/500)
= 255/500 = 51/100
j.
Based on your answers, are variables 1 and 2 independent? Why or why not?
not independent as the probabilities differ, seen in answer g and h
2) Individuals who want to pursue a career in investment analysis are often encouraged to
obtain the professional designation of Chartered Financial Analyst (CFA). A candidate must
pass three exams to obtain this designation and can take only one exam in a given year. The
results of the exams held and reported by the Institute of Chartered Financial Analysis in The
CFA Study Guide are summarised in the accompanying table.
Exam
Number of candidates writing
Percentage who passed
I
6,588
55
II
3,679
56
III
2,542
76
Total
12,809
One candidate is selected at random from those who took a CFA exam.
a). What is the probability that the selected candidate passed?
b). What is the probability that the selected candidate took Exam I and passed?
c).
If the selected candidate passed, what is the probability that the candidate
took Exam III?
*3) Suppose A and B are two mutually exclusive events for which P(A) = .3 and P(B) = .4
Thus P (A and B) = 0. (The condition for mutually exclusive events)
a.
?
Find P(A and B)
b.
Find P(A or B)
= 0.12
c.
Are A and B independent events? Explain using probabilities
0/0.4 does not equal 0.3
*4) A survey conducted by Roy Morgan Research asked 1116 Australians to nominate health issues
they consider important. Sixty per cent of respondents nominated cancer as an important health
issue, and 29 per cent nominated heart disease. Assume that these percentages are true for the
population of Australia and that 25 per cent of all respondents mentioned both cancer and heart
disease as important health issues. What is the probability that a randomly selected Australian:
2
a. Does not nominate cancer as an important health issue?
40%
b. Does not nominate heart disease as important health issue?
71%
c. Nominates cancer and not heart disease as an important health issue?
35%
d. Nominates either cancer or heart disease as an important health issue?
39%
e. Nominates neither cancer nor heart disease as an important health issue?
36%
f. Nominates cancer as an important issue given the person nominated heart disease as an
important issue?
25/29
g. Are choosing heart disease and cancer as important issues dependant?
?
IN QUIZ *5) A hardware store determines that 70% of its customers do not use the selfcheckout system to make their purchases. It also determines that 80% of its customers pay by
cash. Among those using the self-checkout system, however, only 60% pay by cash. Use this
information to determine
a. The probability that a customer uses the self-checkout system.
30%
b. The probability that a customer does not pay by cash.
20%
c. The probability that a customer uses the self-checkout system and pays by cash.
18%
d. The probability that a customer does not use self-checkout system given he or she is
paying by cash.
62/80
e. The probability that a customer pays by cash if the customer uses self-check system.
60%
f. Whether use of the self-checkout system and payment by cash are independent.
no?
3
Chapter 5
1) The following data are from a historical study of the number of flaws found in a porcelain
cup produced by a manufacturing company. Use these data and the associated probabilities
to compute the mean and the standard deviation of the number of flaws. Explain your
findings.
x
P(x)
0
0.461
1
0.285
2
0.129
3
0.087
4
0.038
2) Solve the following problems by using the binomial tables (Table E.6 in Berenson text).
a. If n = 20 and p = .50, find P(x = 12).
b. If n = 20 and p = .30, find P(x > 8).
c. If n = 20 and p = .70, find P(x < 12).
d. If n = 20 and p = .90, find P(x ≤ 16).
e. If n = 15 and p = .40, find P(4 ≤ x ≤ 9).
f. If n = 10 and p = .60, find P(x ≥ 7).
3) Find the mean and standard deviation of the relevant binomial distribution where n =20 and
p=0.70
*4) The probability that a restaurant will fail in its first year of operation has been estimated
to be 0.60. If 10 new restaurants are established in the Illawarra during 2019:
a) What is the probability that exactly 6 of the new restaurants will fail within one year?
0.2508
b) What is the probability that more than 10 of the new restaurants will fail within one year?
not possible, sample size 10
c) What is the probability that less than 8 of the new restaurants will fail within one year?
4
0.2150+0.2508+0.2007+0.115+0.0425+0.0106+0.0016+0.0001 = 0.8417
d) What is the probability that at most 4 of the new restaurants will fail within one year?
0.115+0.0425+0.0106+0.0016+0.0001=0.1752
e) What is the probability that at least 4 of the new restaurants will fail within one year?
1-0.1752=0.8248 ?
f) What is the probability that more than 4 of the new restaurants will fail within one year?
?
g) What is the probability that 3 to 5 (exclusive) of the new restaurants will fail within one
year?
?
h) What is the probability that 3 to 5 (inclusive) of the new restaurants will fail within one
year?
?
i) Calculate the mean and standard deviation of the distribution
E(x)= 10 * 0.6 = 6
VAR= 10*0.6 * (1-0.6) = 2.4
SD = 1.549 (3dp)
5