STAT 400
Final Exam Practice Problems
1. A chain of video stores sells three different brands of VCRs. Of it’s VCR sales, 60%
are brand 1 (the least expensive), 30% are brand 2, and 10% are brand 3.
Each
manufacturer offers a 1year warranty on parts and labor. It is known that 25% of brand
1 VCRs require warranty work, whereas the corresponding percentages for brands 2
and 3 are 20%, 10%, respectively.
(a) What is the probability that a randomly selected purchaser has bought a brand 1
VCR and the VCR will need repair while under warranty?
(b) What is the probability that a randomly selected purchaser has a VCR that will
need repair under warranty?
(c) If a customer returns to the store with a VCR that needs warranty repair work,
what is the probability that it is a brand 1 VCR?
2.
(a) Suppose that math SAT scores for a particular population are normally distributed
with mean 470 and a standard deviation of 100.
i. Find the 33rd percentile,
π
0
.
33
.
ii. Given a random sample of size
n
= 10 scores, find
P
(450
<
¯
X <
550).
(b) Suppose
X
1
, X
2
,
· · ·
, X
16
is a random sample of size 16 from
N
(0
,
1). Determine
c
, such that
P
ˆ
16
X
i
=1
X
2
i
< c
!
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 Spring '05
 TBA
 Statistics, Normal Distribution, Probability, 20%, 25%, 2%, 1year, South Indian River

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