商务统计学-2015期中考试卷
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《商务统计》期中考试试题
Part I: 单选题
(每题2分，共60分)
1. The universe or
a) a
sample.
b) a population.
c) a parameter.
d) a statistic.
2. Which of the
following is most likely a population as opposed
to a sample?
a) respondents to a newspaper
survey.
b) the first 5 students completing an
assignment.
c) every third person to arrive at
the bank.
d) registered voters in a county.
3. A study is under way in Yosemite
National Forest to determine the adult height of
American
pine trees. Specifically, the study
is attempting to determine what factors aid a tree
in
reaching heights greater than 60 feet tall.
It is estimated that the forest contains 25,000
adult
American pines. The study involves
collecting heights from 250 randomly selected
adult
American pine trees and analyzing the
results. Identify the variable of interest in the
study.
a) The age of an American pine tree in
Yosemite National Forest.
b) The height of an
American pine tree in Yosemite National Forest.
c) The number of American pine trees in
Yosemite National Forest.
d) The species of
trees in Yosemite National Forest.
4. The
British Airways Internet site provides a
questionnaire instrument that can be answered
electronically. Which of the 4 methods of data
collection is involved when people complete
the questionnaire?
a) Published sources
b) Experimentation
c) Surveying
d)
Observation
5. To monitor campus
security, the campus police office is taking a
survey of the number of
students in a parking
lot each 30 minutes of a 24-hour period with the
goal of determining
when patrols of the lot
would serve the most students. If X is the number
of students in the
lot each period of time,
then X is an example of
a) a categorical
random variable.
b) a discrete random
variable.
c) a continuous random variable.
d) a statistic.
6. An insurance
company evaluates many numerical variables about a
person before deciding
on an appropriate rate
for automobile insurance. A representative from a
local insurance
agency selected a random sample of insured
drivers and recorded, X, the number of claims
each made in the last 3 years, with the
following results.
X frequency
1 14
2 18
3 12
4 5
5 1
Referring to the table, how many total claims
are represented in the sample?
a) 15
b) 50
c) 111
d) 250
(For Q7 and Q8) A
survey was conducted to determine how people rated
the quality of
programming available on
television. Respondents were asked to rate the
overall quality from 0
(no quality at all) to
100 (extremely good quality). The stem-and-leaf
display of the data is
shown below.
Stem
Leaves
3 24
4 03478999
5 0112345
6 12566
7 01
8
9 2
7.
Referring to the table, what percentage of the
respondents rated overall television quality
with a rating of 80 or above?
a) 0
b)
4
c) 96
d) 100
8. Referring to
the table, what percentage of the respondents
rated overall television quality
with a rating
between 50 and 75?
a) 11
b) 40
c) 44
d) 56
(For Q9 and Q10) The
following are the durations in minutes of a sample
of long-distance
phone calls made reported by
one long-distance carrier.
Time (in Minutes)
Relative Frequency
0 but less than 5 0.37
5 but less than 10 0.22
10 but less than
15 0.15
15 but less than 20 0.10
20 but
less than 25 0.07
25 but less than 30 0.07
30 more 0.02
9. Referring to the
table, if 1,000 calls were randomly sampled, how
many calls lasted under
10 minutes?
a) 220
b) 370
c) 410
d) 590
10.
Referring to the table, if 100 calls were randomly
sampled, how many calls lasted 15
minutes or
longer?
a) 10
b) 14
c) 26
d) 74
11. You have collected data on the
approximate retail price (in $$) and the energy
cost per year
(in $$) of 15 refrigerators.
Which of the following is the best for presenting
the data?
a) A pie chart.
b) A scatter
diagram.
c) A Pareto diagram.
d) A
contingency table.
(For Q12 and Q13) The
histogram below represents scores achieved by 200
job applicants on a
personality profile.
0
.30
.
0.20
0.200.200.20
0.10
0.100.
100.100.10
0.00
010
2030
40
506070<
br>
12. Referring to the histogram, ________
percent of the job applicants scored between 10
and
20.
10%
20%
30%
40%
13. Referring to the histogram, the
number of job applicants who scored between 30 and
below
60 is _______.
a) 20
b) 40
c) 60
d) 80
14. Which measure of
central tendency can be used for both numerical
and categorical
variables?
a) Arithmetic
mean.
b) Median.
c) Mode.
d) Standard
deviation.
15. Which of the following
statements about the median is not true?
a) It
is more affected by extreme values than the
arithmetic mean.
b) It is a measure of central
tendency.
c) It is equal to Q2.
d) It is
equal to the mode in bell-shaped
16. When
extreme values are present in a set of data, which
of the following descriptive
summary measures
are most appropriate:
a) CV and range.
b)
arithmetic mean and standard deviation.
c)
interquartile range and median.
d) variance
and interquartile range.
17. A
probability distribution is an equation that
a) associates a particular probability of
occurrence with each outcome in the sample
space.
b) measures outcomes and assigns
values of X to the simple events.
c) assigns a
value to the variability in the sample space.
d) assigns a value to the center of the sample
space.
18. In a binomial distribution
a) the random variable X is continuous.
b)
the probability of event of interest
is
stable from trial to trial.
c) the number of
trials n must be at least 30.
d) the results
of one trial are dependent on the results of the
other trials.
a)
b)
c)
d)
19. A lab orders 100 rats a week for
each of the 52 weeks in the year for experiments
that the
lab conducts. Prices for 100 rats
follow the following distribution:
Price:
$$10.00 $$12.50 $$15.00
Probability: 0.35 0.40
0.25
How much should the lab budget for next
year’s rat orders be, assuming this distribution
does not change?
a) $$520
b) $$637
c) $$650
d) $$780
20. A multiple-
choice test has 30 questions. There are 4 choices
for each question. A student
who has not
studied for the test decides to answer all
questions randomly. What type of
probability
distribution can be used to figure out his chance
of getting at least 20 questions
right?
a)
binomial distribution.
b) Poisson
distribution.
c) normal distribution.
d)
none of the above.
21. In its
standardized form, the normal distribution
a)
has a mean of 0 and a standard deviation of 1.
b) has a mean of 1 and a variance of 0.
c)
has an area equal to 0.5.
d) cannot be used to
approximate discrete probability distributions.
22. For some positive value of Z, the
probability that a standard normal variable is
between 0
and Z is 0.3340. The value of Z is
a) 0.07
b) 0.37
c) 0.97
d) 1.06
23. The owner of a fish market determined that
the average weight for a catfish is 3.2 pounds
with a standard deviation of 0.8 pound. A
citation catfish should be one of the top 2% in
weight. Assuming the weights of catfish are
normally distributed, at what weight (in pounds)
should the citation designation be
established?
a) 1.56 pounds
b) 4.44 pounds
c) 4.84 pounds
d) 5.20 pounds
24.
If a particular batch of data is approximately
normally distributed, we would find that
approximately
a) 2 of every 3
observations would fall between
1
standard deviation around the mean.
b) 4 of
every 5 observations would fall between
1.28 standard deviations around the mean.
c) 19 of every 20 observations would fall
between
2 standard deviations around the
mean.
d) All the above.
25. Which of
the following about the binomial distribution is
not a true statement?
a) The probability of
event of interest must be constant from trial to
trial.
b) Each outcome is independent of the
other.
c) The random variable of interest is
continuous.
d) Each outcome may be classified
as either
interest.
26. Why is the
Central Limit Theorem so important to the study of
sampling distributions?
a) It allows us to
disregard the size of the sample selected when the
population is not
normal.
b) It allows us
to disregard the shape of the sampling
distribution when the size of the
population
is large.
c) It allows us to disregard the
size of the population we are sampling from.
d) It allows us to disregard the shape of the
population when n is large.
27. Suppose a
sample of n = 50 items is drawn from a population
of manufactured products and
the weight, X, of
each item is recorded. Prior experience has shown
that the weight has a
probability distribution
with
= 6 ounces and
= 2.5
ounces. Which of the following is
true about
the sampling distribution of the sample mean if a
sample of size 15 is selected?
a) The mean of
the sampling distribution is 6 ounces.
b) The
standard deviation of the sampling distribution is
2.5 ounces.
c) The shape of the sample
distribution is approximately normal.
d) All
of the above are correct.
28. For some
positive value of X, the probability that a
standard normal variable is between 0
and +2X
is 0.1255. The value of X is
a) 0.99
b)
0.40
c) 0.32
d) 0.16
29. A campus
program evenly enrolls undergraduate and graduate
students. If a random sample
of 4 students is
selected from the program to be interviewed about
the introduction of a new
fast food outlet on
the ground floor of the campus building, what is
the probability that all 4
students selected
are undergraduate students?
a) 0.0256
b)
0.0625
c) 0.16
d) 1.00
30. If two
events are collectively exhaustive, what is the
probability that both occur at the same
time?
a) 0.
b) 0.50.
c) 1.00.
d) Cannot
be determined from the information given.
Part II: 计算题:
Q1. 某证券公司为了分析上市公司股票价格与公司净资产收
益率的关系，收集了各个上市公
司的财务数据。现有5个家电公司上年的净资产收益率和本年平均股票价
格数据如下：
公司 净资产收益率（％） 本年平均股票价格（元）
A 3.9 6.2
B 1.2 5.3
C 1.4 5.6
D 6.4 8.0
E
4.1 6.8
根据表中给出的数据，计算这些家电公司净资产收益率和公司平均股票价格之间的协方差
（10分）。
Q2. 一家商业银行为了改进中午12点到13点间的客户服务水平，提出了一套改进的服务流
程。下表是在一个星期的12点到13点中随机采样的30个客户的等待时间（分钟）：
X
i
:
0.4 0.5 0.5 0.6 2.3
2.4 2.9 3 3.1 3.2
3.5 3.6 3.8 3.9 4.1 4.2 4.4
4.5 4.7 4.8
5 5.1 5.1 5.2 5.6 5.7 6.1 6.1 6.2
6.2
i
X
i
= 116.7,
i
(X
i
- )
2
= 88.627
a. 计算均值、中位数和众数。 (3分)
b.
计算标准差、全距、变异系数、最大样本和最小样本的 Z值。(5分)
c.
用五值概括法描述等待时间 (5分)
d. 等待时间中有异常值吗?为什么？ (2分)
Q3. 多曼批发商公司的董事长认为公司30%的订单来自新的或第一次合作的客户，该公司用
100个订单的简单随机样本来估计新的或第一次合作的客户所占的比例。
a.
该研究中的p̅的抽样分布是什么？为什么？(5分)
b.
样本比例落在总统比例p=0.30的±0.05范围之内的概率是多少？(5分)
c.
当样本容量为500时，回答问题(b)。(5分)