Test 1 Review Questions
EC 351
Hammond
1. Math SAT scores are distributed normally with
(500,10000)
N
.
(a)
What fraction of students scores above 750? Above 600? Between 420 and 530? Below
480? Above 530?
(b)
Assume that you had chosen 25 students at random who had taken the SAT exam. Derive
the distribution for their average math SAT score. What is the probability that this
average is above 530? Why is this so much smaller than your answer in (a)?
(c)
Verbal SAT scores are also distributed normally with
(500,10000)
N
.
If the math and
verbal scores were independently distributed (which is not a realistic assumption) then
what would be the distribution of the overall SAT score? Find its mean and variance.
(d)
Next, assume that the correlation coefficient between the math and verbal scores is 0.75.
Find the mean and variance of the resulting distribution.
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2. Following Alfred Nobel’s will, there are five Nobel Prizes awarded each year. These are for
outstanding achievements in Chemistry, Physics, Physiology or Medicine, Literature, and Peace.
In 1968, the Bank of Sweden added a prize in Economic Sciences in memory of Alfred Nobel.
The accompanying table lists the joint probability distribution between recipients in economics
and the other five prizes, and the citizenship of the recipients, based on the 19692001 period.
Joint Distribution of Nobel Prize Winners in Economics and NonEconomics
Disciplines, and Citizenship, 19692001
U.S. Citizen
(
0
Y
)
NonU.S. Citizen
(
1
Y
)
Total
Economics Nobel
Prize (
0
X
)
0.118
0.049
0.167
Physics, Chemistry,
Medicine, Literature,
and Peace Nobel
Prize (
1
X
)
0.345
0.488
0.833
Total
0.463
0.537
1.00
(a)
Compute
(
)
E Y
.
(b)
Calculate
(

1)
E Y
X
and
(

0)
E Y
X
.
(c)
A randomly selected Nobel Prize winner reports that he is a nonU.S. citizen. What is the
probability that this genius has won the Economics Nobel Prize? A Nobel Prize in the
other five disciplines?