※ [本文轉錄自 NTUIB94 看板]
作者: EETammy (貝殼) 看板: NTUIB94
標題: 孫立群去年的統計第一次期中考考題
時間: Tue Oct 29 17:14:55 2002
STATISTICS
FIRST MIDTERM EXAM
(Oct.24,2001)
NOTE
1. You should answer each question in detail. Any answer with no
explanation or calculation procedure will receive 0 point.
2. If you don't feel very comfortable about your English writing
ability, you are more than welcome to answer the question(s) in 中文.
3. Please do your own work. The usual University Guidelines on this matter
apply.
Part one : In Class Exam(50 points total)
1. 8 points (3+2+3)
A time study is conducted to determine the length of time necessary to perform
a specified operation in a manufacturing plant. The length of time necessary to
complete the operation is measured for each of n=40 workers.
The mean and variance are found to be 12.8and 2.89, respectively. Describe the
sample data by using the Empirical Rule. Under what kind of conditions can we
describe the data by Tchebysheff's Theorem? What will be the results?
2. 6 points(3+3)
Consider a sample of n=13
97 54 110 27 61 15 69 71 57 73 65 125 76
Please determine the interquartile range and the 8th decile.
3. 6 points(3+3)
There are 75young people in our community. Their ages are as follows:
-------------------------------------------------------------------
Age | 9-11 | 12-14 | 15-17 | 18-20 | 21-23 | 24-26 ｜
------------------------------------------------------------------
Frequency | 15 | 30 | 15 | 10 | 3 | 2 ｜
-------------------------------------------------------------------
Please determine the mean and the median.
4. 8 points(2+2+2+2)
We know that the mean and variance of a set of test scores based on a total of
100 points are 74 and 64 , respectively. Suppose your test grade is 92,what is
the Z value associated with your grade? What's the meaning of that specific Z
score? How will we standardize the set of test scores? What will be the
results after the standardization?
5. 10 points(2 x 5)
A mail order merchandiser of clothing sells two product lines, one relatively
expensive, the other is inexpensive. Asurvey of orders produced the relative
frequencies of orders by product line and the sex of the customer. In the
following table, A is the event that the customer is female and B is the event
that hte order is from product line 1. Suppose that a customer who has
placed an order is selected at random.
-----------------------------------------------------------
｜ ｜ Product line 1 (B) ｜ Product line 2(B')｜
-----------------------------------------------------------
｜ Female(A) ｜ 0.516 ｜ 0.205 ｜
-----------------------------------------------------------
｜ Male(A') ｜ 0.132 ｜ 0.147 ｜
-----------------------------------------------------------
(1)Find the probability that the customer is male
(2)Find the probability that the order is from product line 1 and the customer
is female:
(3)Find the probability that the customer is female or the order is from
product line 1, or both:;
(4)Are A and B independent events?
(5)Find P(B|A) and explain the meaning of it.
6. 12 points(4x3)
JJJ medical institute has developed a diagnostic technique to detect AIDS.
Experimental data show that if a person actually has. AIDS and the probability
that the test will indicate the presence of AIDS is 0.9. Suppose 5% of the
population of a specific country have AIDS.
(1)Please construct the probability tree.
(2)If a person is tested to have AIDS, what is the probability that he is
actually infected by AIDS.
(3)Is the diagnostic technique a very accurate one? Why?
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