A consumer organization that evaluates new automobiles customarily reports the n
ID: 3432320 • Letter: A
Question
A consumer organization that evaluates new automobiles customarily reports the number of major defects in each car examined. Let X denote the number of major defects in a randomly selected car of a certain type. The cdf of X is as follows:
F(x) =
0
0.01
0.24
0.35
0.64
0.87
0.95
1
x < 0
0 ? x < 1
1 ? x < 2
2 ? x < 3
3 ? x < 4
4 ? x < 5
5 ? x < 6
6 ? x
Calculate the following probabilities directly from the cdf:
(a) p(2), that is, P(X = 2)
(b) P(X > 3)
(c) P(2 ? X ? 5)
(d) P(2 < X < 5)
F(x) =
0
0.01
0.24
0.35
0.64
0.87
0.95
1
x < 0
0 ? x < 1
1 ? x < 2
2 ? x < 3
3 ? x < 4
4 ? x < 5
5 ? x < 6
6 ? x
Explanation / Answer
(a) p(2), that is, P(X = 2) =0.35-0.24 = 0.11
--------------------------------------------------------------------------------------------------------------------
(b) P(X > 3) =1-0.35 =0.65
--------------------------------------------------------------------------------------------------------------------
(c) P(2 <= X <= 5) = 0.95-0.24 = 0.71
--------------------------------------------------------------------------------------------------------------------
(d) P(2 < X < 5) = 0.87-0.24 =0.63
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