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Statistics 104: Quantitative Methods for Economists
Fall 2010
Final Examination
Directions
This exam is open book/open notes. Calculators are allowed but not laptop computers.
The exam will end 3 hours after it begins. The exam is divided into two parts. The first part is multiple
choice and true/false. Please answer these questions on the exam by circling the
best
answer (some
rounding occurs in several places). The second part of the exam consists of several problems. Please
answer these problems in the space provided on the exam (you may use the backs of the sheets if
necessary). You will get partial credit for these problems
provided
that your answers are organized and
legible so that your train of thought can be easily followed.
Good Luck
By
Printing
my name below I acknowledge that Harvard has an honor code and that I will adhere to it.
Failure to abide by the honor code could result in failing this course and having to wash Professor
Parzen’s car with my toothbrush.
NAME
: _____________Keyser Soze_______________________________ (50 if not printed)
Question
Points
Obtained
Multiple Choice
100
Long 1
5
Long 2
18
Long 3
12
Long 4
Long 5
Total
165
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Multiple Choice (3 points each)
1)
The standard deviation of the normal distribution shown above is approximately
a)
σ = 100
b) σ = 90
c
) σ = 15
d) σ = 10
2)
As the degrees of freedom for the
t
distribution increase, the distribution approaches
a)
The value of zero for the mean.
b)
The
t
distribution.
c)
The normal distribution
.
d)
The binomial distribution.
3)
Which of the following statements about the Central Limit Theorem (CLT) is correct?
a)
The CLT states that the sample mean
x
is always equal to the population mean,
.
b)
The
CLT
states
that
the
sampling
distribution
of
the
sample
mean
x
is
approximately normal for large sample sizes (
30
n
).
c)
C) The CLT states that the sample mean
x
is equal to the population mean
, provided
that
n
.
d)
D) The CLT states that the sampling distribution of the population mean
is
approximately normal, provided that
n
3
An elevator serving a hospital is designed to hold up to 15 passengers and has a maximum safe capacity
of 2440 pounds. The weight of passengers who use the elevator is normallydistributed with an average of
149 pounds and a standard deviation of 20 pounds.
4)
What is the probability that a single passenger on the elevator weighs between 140 and 150
pounds?
(a)
.1736
(b) .1537
(c) .2236
(d) .1936
(e) .1915
5)
What is the probability that a single passenger on the elevator weighs more than 200 pounds?
(a)
.9946
(b) .4946
(c) .0054
(d) .5054
(e) .9954
6)
If five passengers enter the elevator together, what is the probability that all five of them weigh
200 pounds or less?
(a) .9512
(b) .9734
(c) .9786
(d) .0264
(e)
0.05
7)
What is the probability that the elevator's safe capacity is exceeded by a full load of 15
passengers?
(a) 1.0
(b) 2.65
(c) .0041
(d) 0
(e) .0137
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The mean length of stay in a hospital is useful for planning purposes. Suppose that the following is the
distribution of the length of stay in a hospital after a minor operation.
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.
 Fall '11
 MichaelParzen
 Statistics

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