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Practice Questions for Midterm I, Math 308/608 Spring 2010
1)
The SAT math scores across the population of high school seniors follow a normal
distribution with mean 500 and standard deviation 100.
a)
If five seniors are randomly selected, what is the distribution of the
sum
of their scores?
b)
If five seniors are randomly selected, what is the distribution of the
average
of their
scores?
2)
A random sample of 300 CitiBank VISA cardholder accounts indicated a sample mean debt
of $1220 with a sample standard deviation of $840.
Construct an approximate 95%
confidence interval for the average debt of all cardholders, using the fact that P(
Z
> 1.96) =
0.025 for a standard normal random variable
Z
.
3)
Suppose that
X
is discrete random variable with the following probability mass function:
3
(1
),
(2
(3
)
1
.
24
4
PX
θ
θθ
==
= =
==−
We observe a sample of size 5 with values
x
= (1, 2, 2, 3, 3).
a)
Find the method of moments estimate of
.
b)
Find the maximum likelihood estimate of
.
4)
A random sample of 1200 engineers included 204 females.
Find a 90% confidence interval
for the proportion of all engineers who are female, using the fact that P(
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This note was uploaded on 06/12/2010 for the course MATH 308 taught by Professor Lacey during the Spring '10 term at Tulane.
 Spring '10
 LACEY
 Normal Distribution, Standard Deviation

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