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Solved: Let X denote the amount of space occupied by an
Chapter 4, Problem 15E(choose chapter or problem)
Problem 15E
Let X denote the amount of space occupied by an article placed in a 1-1ft3 packing container. The pdf of X is
a. Graph the pdf. Then obtain the cdf of X and graph it.
b. What is P(X≤.5)
c. Using the cdf from (a), what is P(.25 < X ≤ .5)? What is P(.25 ≤ X ≤ .5)?
d. What is the 75th percentile of the distribution?
e. Compute E ( X ) and σ x .
f. What is the probability that X is more than 1 standard deviation from its mean value?
Questions & Answers
QUESTION:
Problem 15E
Let X denote the amount of space occupied by an article placed in a 1-1ft3 packing container. The pdf of X is
a. Graph the pdf. Then obtain the cdf of X and graph it.
b. What is P(X≤.5)
c. Using the cdf from (a), what is P(.25 < X ≤ .5)? What is P(.25 ≤ X ≤ .5)?
d. What is the 75th percentile of the distribution?
e. Compute E ( X ) and σ x .
f. What is the probability that X is more than 1 standard deviation from its mean value?
ANSWER:
Answer:
Step1:
Let X denote the amount of space.
Step2:
a). To obtain the cdf of X .
F(x) = 0 for
F(x) = 0 for x = 1.
Therefore,
F(x) =
=
F(x) = 90
= 90
= 90[-
= 90[
= 90[
F(x) =
Step3:
b). To find P(x)
= F(x) =
= F(0.5) = 10
= 0.01953-0.0088
= 0.0108
Therefore, = 0.0108.
Step4:
c). i) To find P(0.25 < X 0.5).
P(0.25 < X 0.5) =
= [1-P(x <0.25)] -
= (1-F(0.25)) - F(0.5)
F(0.5) 10
0.0108