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※ 引述《ckwool (期中考)》之銘言：
課程名稱︰統計學甲上
課程性質︰工管系必修
課程教師︰蔣明晃
開課系所︰工管系
考試時間︰2004.10~11月
試題 :
Multiple Choices Questions:(each 2.5 points; total 100 points)
1.You asked five of your classmates about their height. On the basis of this
information, you stated that the average height of all students in your
university or college is 67 inches. This is an example of:
a. descriptive statistics
b. statistical inference (ˇ)
c. parameter
d. population
2.Which of the following statements is false?
a. A frequency distribution counts the number of observations that fall into
each of a series on intervals, called classes that cover the complete range of
observations.
b. The intervals in a frequency distribution may overlap to ensure that each
observation is assigned to an interval. (ˇ)
c. Although the frequency distribution provides information about how the
numbers in the data set are distributed, the information is more easily
understood and imparted by drawing a histogram.
d. The number of class intervals we select in a frequency distribution depends
entirely on the number of observations in the data set.
3.The total area of the bars in a relative frequency histogram:
a. depends on the sample size
b. depends on the number of bar
c. depends on the width of each bar (ˇ)
d. Both a and b
4.Which of the following statements is true?
a. When the distribution is skewed to the left, mean>median>mode
b. When the distribution is skewed to the right, mean<median<mode
c. When the distribution is symmetric and unimodal, mean=median=mode(ˇ)
d. When the distribution is symmetric and bimodal, mean=median=mode
5.Which measure of cen tral location is meaningful when the data are nominal?
a. The arithmetic mean
b. The geometric mean
c. The median
d. The mode (ˇ)
6.Which of the following summary measures is affected most by outliers?
a. The median
b. The geometric mean
c. The range (ˇ)
d. The interquartile range
7.Which of the following summary measures cannot be easily approximately from a
box-and-whisker plot?
a. The range
b. The interquartile range
c. The standard deviation (ˇ)
d. None of all
8.Which of the following statement is false?
a. The standard deviation is expressed in terms of the original units of
measurement but the variance is not
b. In a histogram, the proportion of the total area which must be to the left
of the median is more than 0.50 if the distribution is skewed to the right(ˇ)
c. The length of the box in the box-and-whisker plot portrays the
interquartile range
d. The mean of fifty sales receipts is $65.75 and the standard deviation is
$10.55. Using Chebyshev's theorem, 75% of the sales receipts were between
$44.65 and $86.85.
9. If A and B are mutually exclusive events with P(A)=0.70,then P(B):
a. can be any value between 0 and 1
b. can be any value between 0 and 0.70
c. cannot be larger than 0.30 (ˇ)
d. cannot be determinded with the information given
10.If A and B are independent events with P(A)=0.60 and P(A/B)=0.60 then P(B)
is:
a.1.20
b.0.60
c.0.36
d.Cannot be determined with the information given(ˇ)
11.Assume that you invested $10,000 in each of three stocks. Each stock can
increase in value, decrease in value, or remain the same. Drawing a probability
tree for this experiment will show that the number of possible outcomes is:
a.10,000
b.3
c.9
d.27(ˇ)
12.Which of the following statements is correct given that the events A and B
have nonzero probabilities?
a. A and B cannot be both independent and mutually exclusive (ˇ)
b. A and B can be both independent and mutually exclusive
c. A and B are always independent
d. A and B are always mutually exclusive
13.If A and B are independent events with P(A)=0.60 and P(B)=0.70, then the
probability that A occurs or B occurs or both occurs is:
a. 1.30
b. 0.88 (ˇ)
c. 0.42
d. 0.10
14.Suppose A and B are two independent events for which P(A)=0.20 and P(B)=0.60
a.P(A/B)=0.20
b.P(B/A)=0.60
c.P(A and B)=0.12
d.P(A or B)=0.80 (ˇ)
15.Suppose P(A)=0.50 P(B)=0.40, and P(B/A)=0.30
a.P(A and B)=0.15
b.P(A or B)=0.75
c.P(A/B)=0.375
d.All are corect (ˇ)
16.Suppose P(A^c)=0.30,P(B^c/A)=0.40, and P(B^c/A^c)=0.50
a.P(A and B)=0.42 (ˇ)
b.P(B^c)=0.45
c.Find P(A or B)=0.87
d.All are correct
17.A statistics professor classifies his students according to their grade
point average(GPA) and their gender. The accompanying table gives the
proportion of students falling into the various categories. One student is
selected at random.
GPA
┌────┬─────┬─────┬─────┐
│ Gender │ Under2.0 │ 2.0-3.0 │ Over3.0 │
├────┼─────┼─────┼─────┤
│ Male │ 0.05 │ 0.25 │ 0.10 │
│ Female │ 0.10 │ 0.30 │ 0.20 │
└────┴─────┴─────┴─────┘
a. If the student selected is female, the probability that her GPA is between
2.0 and 3.0?
b. If the GPA of the student selected is over 3.0, the probability that the
student is male is 0.333 (ˇ)
c. The probability that the student selected is female or has a GPA under 2.0
or both is 0.60
d.GPA is independent of gender
18.An investment firm has classified its clients according to their gender and
the composition of their investment portfolio (primarily bonds, primarily
stocks, or a balanced mix of bonds and stocks). The proportions of clients
falling into the various categories are shown in the following table:
Portfolio Composition
┌────┬─────┬─────┬─────┐
│ Gender │ Bonds │ Stocks │ Balanced │
├────┼─────┼─────┼─────┤
│ Male │ 0.18 │ 0.20 │ 0.25 │
│ Female │ 0.12 │ 0.10 │ 0.15 │
└────┴─────┴─────┴─────┘
One client is selected at random, and two events A and B are defined as
follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
a.P(A/B^c)=0.733
b.P(A^c/B)=0.375 (ˇ)
c.A and B^c are inpendent events
d.A and B are indenpent events
19.If X and Y are any random variables, which of the following identities is
not always true?
a.E(X+Y)=E(X)+E(Y)
b.V(X+Y)=V(X)+V(Y) (ˇ)
c.E(4X+5Y)=4E(X)+5E(Y)
d.V(4X+5Y)=16V(X)+25V(Y)+40COV(X,Y)
20.If X and Y are random variable with V(X)=7.5, V(Y)=6, and COV(X,Y)=4, then
V(2X+3Y)is:
a.33
b.37
c.88
d.132 (ˇ)
21.If X and Y are any random variable with E(X)=50,E(Y)=6,E(XY)=21,V(X)=9 and
V(Y)=10, then the relationship between X and Y is a:
a. strong positive relationship
b. strong negative relationship (ˇ)
c. weak positive relationship
d. weak negative relashinship
22.The probability distribution of a discrete random variable X is shown below:
┌────┬─────────────────┐
│ x │ 0 1 2 3 │
├────┼─────────────────┤
│ p(x) │ 0.25 0.40 0.20 0.15 │
└────┴─────────────────┘
a. E(X-2)=1.75
b. V(3X-2)=8.87
c. E(2X^2+3X-1)=7.85 (ˇ)
d. E(2X^2+5)=9.1
23.The joint probability distribution of variables X and Y is shown in the
table below. X
┌────┬─────────────┐
│ Y │ 1 2 3 │
├────┼─────────────┤
│ 1 │ 0.30 0.18 0.12 │
│ 2 │ 0.15 0.09 0.06 │
│ 3 │ 0.05 0.03 0.02 │
└────┴─────────────┘
a.P(Y=2|X=1)=0.35
b.V(X+Y)=1.06 (ˇ)
c.X and Y are dependent
d.None of all are correct
24.A recent survey in Michigan revealed that 60% of the vehicles traveling on
highways, where speedlimits are posted at 70 miles per hour, were exceeding
the limit. Suppose you randomly record the speeds of ten vehicles traveling on
US 131 where the speed limit is 70 miles per hour. Let X denote the number of
vehicle that were exceeding the limit. Find the following probabilities:
a.P(X=10)=0.01
b.P(4<X<9)=0.85
c.P(X=2)=0.006
d.P(3<=X<=6)=0.606 (ˇ)
25.An advertising executive receives an average of 10 telephone calls each
afternoon between 2 and 4 P.M. The calls occur randomly and independently of
one another.
a. The probability that the executive will receive 13 calls between 2 and 4 P.M
on a particular afternoon is 0.105
b. The probability that the executive will receive seven calls between 2 and 3
P.M on a particular afternoon is 0.072
c. The probalility that the executive will receive at least five calls between
2 and 4 P.M. on a particular afternoon is 0.971
d. None of all are correct (送分)
26. Suppose the following frequency distribution represents the rent paid by 44
tenants in apartments located on the West side of a city:
Class Number Rent in dollars Frequency
1 400 to 500 7
2 500 to 600 10
3 600 to 700 18
4 700 to 800 9
What is the approximate variance of this data sample?
a. 9741.0 (ˇ)
b. 9519.6
c. 97.6
d. 8621.5
27.The yearly wages in a manufacturing company have a bell-shaped distribution
with a mean of $21,000 and a standard deviation of $550. About what percentage
of workers earn less than $20,450 per year?
a. 68
b. 32
c. 50
d. 16 (ˇ)
28.Assuming that each of the 52 cards in an ordinary dexk has a probability of
1/52 of being drawn, what is the probability of drawing an ace and a queen in
succession without replacement?
a.1/26
b.9/13
c.4/663 (ˇ)
d.4/13
29.Team A has a probability of .60 of winning whenever it plays. If A plays
four games, what is the probability that A wins more than half of the games?
a. .500
b. .476 (ˇ)
c. .129
d. .345
30.Many managers are implementing statistical process control to reduce both
common and special causes of accidents on the job. The common causes are those
which are the fault of management and special causes are those that can be
traced back to an individual worker or machine. Experts estimate that 85% of
the problems in the system have common causes and 15% have special causes.
Assume that a certain manager took a random sample of 30 accidents on the job.
What is the probability that this manager finds less than four accidents that
can be traced back to special causes? Use the Poisson approximation.
a. .215
b. .342 (ˇ)
c. .417
d. .553
31.Sam will read either one chapter of his probablity book or one chapter of
his history book. If the number of misprints in a chapter of his probability
book is Poisson distributed with mean 2 and if the number of misprints in his
history chapter is Poisson disstributed with mean 5, then assuming Sam is equally
likely to choose either book, what is the expected number of misprints that
Sam will come across?
a. 2.5
b. 3.5 (ˇ)
c. 4.5
d. 5.5
32. Pollutions of the rivers in the Taiwan has been a problem for many year.
Consider the following event:A={The river is polluted},B={A sample of water
detects pollution},C={Fishing permitted}.Assume:P(A)=0.3,P(B|A)=0.75,
P(B|A^c)=0.20,P(C|A且B)=0.20,P(C|A^c且B)=0.15,P(C|A且B^c)=0.80,
P(C|A^c且B^c)=0.90.
a. P(A且B且C)=0.045 (ˇ)
b. P(B^c且C)=0.63
c. P(C)=0.1064
d. The probability that the river is polluted, given that fishing is permitted
and the sanple test didn't detect pollution is 0.564
33.Consider the density fuction f(x)={k(x^1/2) 0<x<1
{0, elsewhere
a. k=2/3
b. F(x)=x^3/2 (ˇ)
c. P(0.3<x<0.6)=0.6
d. None of all are correct
34.From a sack of fruit containing 3 oranges, 2 apples and 3 bananas a random
sample of 4 pieces of fruit is selected. If X is the number of oranges and Y
is the number of apples in the sample.
a. P{X+Y<=1}=5/70
b. P{X+Y<=2}=3/7
c. P{X+Y<=3}=3/7
d. All of the above are correct
35.If a random variable X is defined such that E[(x-1)^2]=10,E[(x-2)^2]=6
a. E(X)=4
b. E(X^2)=10
c. Var(X)=3.75
d. All of the above are incorrect.
36.A random variable X has a mean 10 and a variance 4. Using Chebyshev's
theorem
a. P(|X-10|>=3)<=5/9
b. P(|X-10|<3)>=4/9
c. P(5<X<15)>=0.84 (ˇ)
d. If P(|X-10|>=c)<=0.04,then c=8
37.Let X represent the number that occurs when a red die is tossed and Y the
number that occurs when a green die is tossed
a. E(X+Y)=7
b. E(X-Y)=0
c. E(XY)=12.25
d. All of the above arecorrect
38.If the probability that a fluorescent light has a useful life of at least
800 hours is 0.9, the probability among 20 such lights
a. exactly 18 will have a useful life of at least 800 hours is 0.2852 (ˇ)
b. at least 15 will have a useful life of at least 800 hours is 0.6083
c. at least 2 will have a useful life of at least 800 hours is 0.9887
d. All of the above are correct
39.Lots of 40 components each are called unacceptable if they contain as many
as 3 defective or more. The procedure for sampling the lot is to select 5
components at random and to reject the lot if a defective is found.
a. the probability that exactly 1 defective is found in the sample if there
are 3defectives in the entire lot is 0.3011
b. the average of number of defectives 0.375
c. the variance of number of defectives is 0.3113
d. all of the above are correct
40.In a certain industrial facility accidents occur infrequently. It is known
that probability of an accident on any given day is 0.005 and accidents are
independent of each other.Given any given period of 400 dats.
a. the probability that there will be an accident on one day is 0.261
b. the probability that there will be no acident on any single day is 0.1353
c. the probability that there will be 2 days with an acident is 0.3907
d. the probability that there will be at most 3 days with an accident is 0.857
(ˇ)
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