课程名称︰统计学一上
课程性质︰必修
课程教师︰郭瑞祥
开课学院：管理学院
开课系所︰工管系
考试日期（年月日）︰104/11/12
考试时限（分钟）：三小时
试题 :
计算填充题(84%)：需写出计算过程
1.(5%) Given: The probabilities of three events, A, B, and C, occurring are
P(A) = 0.35, P(B) = 0.45, and P(C) = 0.2. Assuming that A, B, or C has
occurred, the probabilities of another event, X, occurring are P(X│A)=0.8,
P(X│B)=0.65, and P(X│C)=0.3. Find P(A│X)= _____________.
2.(5%) A Ph.D. graduate has applied for a job with two universities: A and B.
The graduate feels that she has a 60% chance of receiving an offer from
university A and a 50% chance of receiving an offer from university B. If she
receives an offer from university B, she believes that she has an 80% chance
of receiving an offer from university A. What is the probability that at
least one university will make her an offer?
Probability = _________________
3.(5%) The monthly sales at a bookstore have a mean of 50,000 and a standard
deviation of 6,000. Profits are calculated by multiplying sales by 40% and
subtracting fixed costs of 12,000. Find the standard deviation of monthly
profits.
Standard deviation of monthly profits = ____________
4.(5%) Suppose a disease is present in 3% of population. A diagnostic test for
such disease shows 10% false positive and 5% false negative. That is, for a
patient having the disease,, the test shows positive (+) with probability
0.95 and negative (-) with probability 0.05. For a patient not having
disease, the test shows positive (+) with probability 0.10 and negative (-)
with probability 0.90. If a patient’s test show (+), what’s the probability
of his having the disease?
Probability = ______________
5.(6%) Throw a dice n times fairly and observe the number of dice each time.
Assume a random variable X is the frequency that the number of dice is one.
a. (3%) Write down the probability distribution of random variable
X=_______________
b. (3%) Assume n = 5, P(X<=1 or X>=5)=______________
6.(5%) A communication system consists of n components, each of which will,
independently, function with probability p. The total system will be able to
operate effectively if at least one-half of its components function. For what
values of p is a 5-component system more likely to operate effectively than a
3-component system?
Values of p should be ___________
7.(6%) Suppose that earthquake occur in the eastern part of Taiwan in
accordance with the assumptions for the Poisson probability distribution at a
rate of 2 per day.
a. (3%) Find the probability that at least 3 earthquake occur during the next
2 days = _______________
b. (3%) Find the probability distribution of the time, starting from now,
until the next earthquake. _____________________
8.(5%) Suppose that the proportion of colorblind people in a certain
population is 0.005. What is the probability that there will not be more than
one colorblind person in a randomly chosen group of 600 people? You can use
Poisson distribution to approximate the binomial distribution.
Probability = __________________
9.(5%) Suppose the daily amount of waste generated per person is normally
distributed, with mean 3.58 pounds and standard deviation 1.04 pounds. Of the
daily amounts of waste generated per person, 67.72% would be greater than
what amount? ____________________
10.(5%) Suppose that customers arrive at a drive through window at an
average rate of three customers per minute and that their arrival follow the
Poisson model. Use the appropriate distribution to find the probability that
the next customer will arrive within 1.5 minutes.
Probability = ________________
11.(7%) Suppose that patrons of a restaurant were asked whether they preferred
beer or whether they preferred wine. 60% said that they preferred beer. 70% of
the patrons were male. 80% of the males preferred beer.
a.(3%) What is the probability a randomly selected patron prefers wine?
Probability = ____________
b. (3%) Suppose a randomly selected patron is a female. What is the probability
that the patron prefers wine?
Probability = ____________
c. (1%) Are gender of patrons and drinking preference independent?
Choose yes or no = _____________ Explain below.
12.(5%) Suppose that X is a random variable for which E(X)=μ and Var(X)=σ^2.
Find E[X(X-1)]=__________________
13.(5%) Suppose that X and Y are random variables such that Var(X)=9, Var(Y)=4,
and ρ(X,Y)=-1/6. Find Var(X-3Y+4)=______________
14.(5%) The average score of all student in an economics class has a mean of
70 and a standard deviation of 3. Suppose a sample of 36 students took the
class this semester. Find the probability that the average score of the 36
students exceeded 71.
Probability = _____________
15.(5%) The chairman of the statistics department in a certain college believes
that 70% of the department’s graduate assistantships are given to
international students. A random sample of 50 graduate assistants is taken.
What is the probability that the sample proportion p` will be within ±.05 of
the population proportion p`?
Probability = ________________
16.(5%) Suppose that the starting salaries of finance graduates from
university A are normally distributed with a mean of $36,750 and a standard
deviation of $5,320. The starting salaries of finance graduates from
university B are normally distributed with a mean of $34,625 and a standard
deviation of $6,540. If simple random samples of 50 finance graduates are
selected from each university, what is the probability that the sample mean
of university A graduates will exceed that of university B graduates?
Probability = _______________
选择题 (16%)
17.Which of the following statements is true?
a. The sum of the deviation from the arithmetic mean is always zero
b. The sum of the squared deviations from the arithmetic mean is always zero
c. The range mean is always smaller than the variance
d. The standard deviation is always smaller than the variance
18.When studying the simultaneous responses to two categorical questions, we
should develop a
a. contingency table
b. frequency distribution table
c. cumulative percentage distribution table
d. histogram
19.Which of the following statements is true for the following data values:
7, 5, 6, 4, 7, 8, and 12?
a. The mean, median and mode are all equal
b. Only the mean and median are equal
c. Only the mean and mode are equal
d. Only the median and mode are equal
20.In left-skewed distributions, which of the following is the correct
statement?
a. The distance from Q_1 to Q_2 is smaller than the distance from Q_2 to Q_3
b. The distance from the smallest observation to Q_1 is larger than the
distance from Q_3 to the largest observation
c. The distance from the smallest observation to Q_2 is smaller than the
distance from Q_2 to the largest observation
d. The distance from Q_1 to Q_3 is twice the distance from Q_1 to Q_2
21.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. Mean and standard deviation
c. Interquartile range and median
d. Variance and interquartile range
22.A standard deck of cards is being used to play a game. There are four suits
(hearts, diamond, clubs, and spades), each having 13 cards (ace, 2, 3, 4, 5,
6, 7, 8, 9, 10, jack, queen, and king), making a total of 52 cards. This
complete deck is thoroughly mixed, and you will receive the first two cards
from the deck without replacement. What is the probability that both cards
are queens?
a. 12/2652
b. 16/2652
c. 156/2652
d. None of the above
23.Which of the following statements is correct?
a. If P(A∩B)=0, then A and B are independent events
b. If A and B are independent events, then P(A)=P(A│B)
c. If X follows normal distribution, then for any x, P(X=x)=0
d. If A and B are two events, then P(A)=P(A∩B)+P(A∩B')
24.Like the normal distribution, the exponential density function f(x)
a. is bell-shaped
b. is symmetrical
c. approaches infinity as x approaches zero
d. approaches zero as x approaches infinity
Solution:
计算填充题
1. 0.4427
2. 0.7
3. 2400
4. 0.2271
5. (a) B(n,p=1/6) (n) (1/6)^x (5/6)^(n-x), x=0,1,…,n
(x)
(b) b=0.8839
6. p>1/2
7. (a) 0.7619
(b)2[e^(-2x)], x>=0
8. 0.1992
9. 3.1016
10. 0.9889
11. (a) 0.4
(b) 0.867
(c) No
12. σ^2+μ^2-μ
13. 51
14. 0.0228
15. 0.5588
16. 0.9625
选择题
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