QUIZ 5
AMS310.01
Monday, October 20, 2003
Print your name here________________________________________________
____1.
Suppose that X has mean
μ
=10 and
σ
=50 and Y= (X10)/50. The mean of
Y equals_____
____2.
Suppose that X is a binomial variable with n=81 and p=0.5.
Then
μ
=np= 40.5 and
σ
=
=

)
1
(
p
np
5
.
0
5
.
0
81
x
x
= 4.5.
Then Pr(X
≤
49)
2245
P(Z
≤
____) =
Φ
(z)
. Find z.
34.
Suppose X is a
continuous
random variable with normal histogram.
Suppose also that the mean value of X equals 5 and the standard
deviation of X equals 3, i.e.,
μ
=5 and
σ
=3
____3. Pr{ X <
0}= _______.
Hint: Find z.
Pr(X<0)=
Φ
(z).
____4. Find the 95
th
percentile for X, i.e. Find c such that P(X<c) = 0.95.
Hint :
Φ
(1.96) = 0.95.
Extra Credit: When are Dr. Mendell's office hours?
Do you have a class conflicting
with both of Dr. Mendell's office hours?
Yes____
No_____.
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Solutions to Quiz 5
__0.0__
1.
Suppose that X has mean
μ
=10
σ
=50 and Y= (X10)/50. The mean of Y equals_____
The mean of Y= 0.0.
Y= (X
μ
)/
σ
= Z score.
Mean of Z score = 0.0
and Standard deviation of Z score = 1.0 always.
__2.0 (1/2 credit for 1.89 or 17/9)
__
2.
Suppose that X is a binomial variable with n=81 and p=0.5. Then
μ
=np=40.5 and
σ
=
=

)
1
(
p
np
5
.
0
5
.
0
81
x
x
= 4.5.
Then Pr(X
≤
49)
2245
P(Z
≤
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 Fall '03
 Mendell
 Normal Distribution, Standard Deviation, Probability theory, Dr. Mendell

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