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Business Statistics, ISOM2500 (L3, L4 & L5)
Practice Quiz I
1. The following bar chart describes the results of a survey concerning the relevance of study to present
job by school.
Focus on the School of Business and Management. What are the mode and the median respectively?
(a) Relevant, Neutral
(b) Relevant, Relevant
(c) Neutral, Relevant
(d) Neutral, Neutral
2-4. The manager of a specialty outdoor store has gathered the following data concerning sales (in
hundreds of dollars) of all the items sold by the store in the previous 2 months:
Item Type
pants and jackets
hats and gloves
socks and shoes
skiing hardware
climbing hardware
Number sold
150
30
75
25
70
Sales $(00s)
125
15
400
65
45
2. Using the data along with appropriate computations, which of the following could not be constructed?
(a) A relative frequency table based on the numbers sold of different item types.
(b) A pie chart for the percentages of sales of different item types.
(c) A bar chart for the sales of hardware for each of the two months.
(d) A Pareto chart for the sales of different item types.
3. What is the percentage of dollar sales for hardware?
(a) 16.9%
(b) 27.1%
(c) 10%
(d) 6.9%
4. Which of the following would be the best choice for showing the share of sales due to each Item
Type?
(a) Mode
(b) Median
(c) Frequency table
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(d) Relative frequency table
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5. Two treatments for kidney stones are compared. The following table summarizes their respective
successive rate for treatments involving both small and large kidney stones
Small Stones
Large Stones
Treatment A
93%
73%
Treatment B
87%
69%
Which of the following statements is false?
(a) Treatment A is more effective when used on small stones.
(b) Treatment A is more effective when used on large stones.
(c) Treatment A must be more effective when considering both sizes at the same time.
(d) It is possible that Treatment A is less effective when considering both sizes at the same time.
6-7. Some graphical descriptions of final examination scores for students of a Statistics course are given
below.
6. Based on the figure above, which statement is false?
(a) The score distribution is left skewed
(b) The interval length for the histogram is 10
(c) There is at least one student who got the perfect score of 100
(d) Among all intervals in the histogram, the highest frequency occurs at 70’s.
7. Based on the figure above, which statement is correct?
(a) There is only one outlying score.
(b) Removing outlier(s) would increase the mean and SD.
(c) The mean score is higher than the median score.
(d) More than 50% of the students scored between 50 and 80.
8. Which scatterplot shows a strong negative association?
(a)
(b)
(c)
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(d)
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9. A survey on all the fires in a big city in the last ten years is conducted, and the relationship between
the number of fire engines at each fire and the damages in dollars at each fire is studied. It is found
that the number of fire engines and the amount of damage is strongly positively correlated. Based
on this finding, which statement is correct?
(a) More fire engines cause bigger damage.
(b) Bigger damages cause more fire engines.
(c) Big damages are typically accompanied with small number of fire engines.
(d) None of the above is correct.
10. A professor gives a quiz with 10 multiple choice questions. After grading the papers, the professor
writes down for each student the number of questions the student got right and the number wrong.
The average number of right answers is 8.13 with an SD of 1.1. What are the average and standard
deviation (SD) of the number of wrong answers?
(a) (1.87, 1.1)
(b) (1.87, 8.9)
(c) (8.13, 1.1)
(d) (8.13, 8.9)
11. Two events with positive probabilities are impossible to have the following relationship:
(a) Independent and mutually exclusive.
(b) Dependent and mutually exclusive.
(c) Independent and Not mutually exclusive.
(d) Dependent and Not mutually exclusive
12. If you roll two fair dice, what is the probability that the sum on the two dice equals 6?
(a) 3/36
(b) 4/36
(c) 5/36
(d) 6/36
13. Based on the following mosaic plot, which of the following statements is false?
(a) P (B) = 0.5
(b) P (B|A) = 0.25
(d) Events A and B are independent.
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(c) P (B|Not A) = 0.75
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14. The human resources manager at a company has classified applicants according to whether or not
they have any computer skills (Yes or No), and whether or not they have previous work experience
(Yes or No). The results are summarized below:
Work Experience
Yes No
Yes 80
40 120
No 60
30 90
140 70 210
Computer skills
Which of the following statements is not correct?
(a) If an applicant is randomly selected and the applicant has previous work experience, then the
probability that the applicant has computer skills is about 0.57
(b) If an applicant is randomly selected, the probability that the applicant has no previous work
experience but has computer skills is about 0.19
(c) The data given above indicate that an applicant having computer skills is independent of the
applicant having previous work experience
(d) If an applicant is randomly selected, the probability that the applicant either has no computer
skill or has no previous work experience is about 0.76
15. A fair coin is repeatedly tossed, and the coin lands heads in all the first 5 tosses. Which of the
following statement concerning the 6th toss is true?
(a) The coin is less likely to land heads than to land tails.
(b) The coin is more likely to land heads than to land tails.
(c) The coin is equally likely to land heads as tails.
(d) None of the above.
16. Suppose that events A and B both have positive probabilities. Which of the following statement is
false?
(a) It is possible that P (A ∪ B) > P (A) + P (B).
(b) It is possible that P (A ∩ B) = P (A) × P (B).
(c) It is possible that P (A ∪ B) < P (A) + P (B).
(d) It is possible that P (A ∩ B) > P (A) × P (B).
17. To promote sales a retailer offers special scratch-off coupons. When the shopper makes a purchase,
the clerk scratches off the covering to reveal the amount of the discount. The discount is 10%, 30%
and 50% of the initial amount. 7/8 of the coupons give the shopper 10% off, 3/32 give 30% off, and
1/32 give 50% off. Suppose that half of the customers purchase a sweater that retails for $100 and
another half purchases a suit that retails for $150. What’s the probability that a randomly selected
customer saves more than $40 by using one of these coupons?
(a) 1/8
(b) 1/16
(c) 5/64
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(d) 3/32
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18. The following plots show the probability distribution functions of four random variables: X, Y, Z
and W .
X
Y
Z
W
Based on these plots, which random variable has the largest SD? (You do not need to compute the
SD from the shown probabilities to answer this question)
(a) X
(b) Y
(c) Z
(d) W
19. A game involving chance is said to be a fair game if the expected amount won or lost is zero. Consider
the following arcade game. A player pays $1 and chooses a number from 1 to 10. A spinning wheel
then randomly selects a number from 1 to 10. If the numbers match, the player wins $x (and gets
his/her $1 back); otherwise the players loses the $1 entry fee. What value should x be so that the
game is fair?
(a) 1
(b) 5
(c) 9
(d) 10
20. A plumber loads his truck each morning with faucets that will be needed for the service calls and
other emergency calls that come in that day. Based on past experience, the number, N , of faucets
required each day has the following distribution: p(0) = 0.05; p(1) = 0.25; p(2) = 0.5; p(3) = 0.15;
p(4) = 0.05. Each faucet requires 25 minutes to install. What is the expected number of minutes
the plumber will spend each day installing faucets?
(a) 26.9
(b) 50
(c) 47.5
(d) 9.5
21. Suppose you roll a fair die 6,000 times, what does the Law of Large Numbers say?
(a) You should expect to get exactly 1,000 times of Ace (i.e., one point).
(b) If after 5,999 flips you have exactly 999 Aces, you should expect the next roll to be an Ace.
(c) It is likely that the average points is close to 3.5.
(d) The next roll has a 1/6 probability of being Ace.
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(ISOM2500)[2012](f)midterm1~=0zvopee^_78631.pdf downloaded by cyleungbr from http://petergao.net/ustpastpaper/down.php?course=ISOM2500&id=0 at 2022-02-27 05:31:45. Academic use within HKUST only.
22-23. A distribution center for a chain of electronics stores receives orders from the various branches.
When an order is received, an amount of time, X, is required to collect the items ordered by the
store, and then an amount of time, Y , is required to load all the items onto a delivery truck. The
characteristics of the two random variables is as follows: E(X) = 1.5 hours, SD(X) = .4 hours;
E(Y )=2.2 hours, SD(Y ) = .5 hours. The correlation between X and Y is ρ = 0.95.
22. About the time required to fill an order (that is, the time required to have the delivery truck loaded
and ready to go) once an order is received at the distribution center, which is correct?
(a) Standard deviation is about 0.9 hours
(b) Variance is 0.41 (hours2 )
(c) It will be on average greater than 4 hours
(d) Variance is smaller than 0.41 (hours2 )
23. The worker who collects the items on the order makes $70 per hour, and the worker who loads the
items into the truck makes $80 per hour. Which of the following is false about the total cost of
filling an order that is received at the distribution center?
(a) The expected total cost is $281
(b) The standard deviation is about $67
(c) The variance is greater than 2384 ($2 )
(d) The standard deviation would be bigger if the correlation between X and Y were 0.5
24. An investor buys the stocks of two companies, investing $10,000 in each. The stock of each company
either goes up by 10% after a month with probability 1/2 or drop by 8% with probability 1/2. The
changes in the two stock prices are positively correlated with correlation 0.7. Which of the following
statements is true?
(a) The expected value of the investment after one month is larger than $20,200
(b) The expected value of the investment after one month is equal to $20,200
(c) The expected value of the investment after one month is smaller than $20,200
(d) Cannot determine based on the given information
25. Consider two investment plans, A and B. Their annual returns have means 65% and 36%, and
standard deviations 132% and 66% respectively. Suppose one wants to choose one plan and invest
for 20 years. Which of the following statements is correct?
(a) Plan A is better because it has a bigger expected return.
(b) Plan B is better because it has a smaller standard deviation.
(c) Plan A is better because it has a higher Sharpe ratio.
(d) Plan B is better because it has a higher volatility-adjusted return.
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