Let X denote the amount of space occupied by an article placed in a 1-ft packing container. The pdf of X is below. -x) 0
Let X denote the amount of space occupied by an article placed in a 1-ft packing container. The pdf of X is below. -x) 0
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.1: Exponential Functions
Problem 3E: (a) To obtain the graph of g(x)=2x1 , we start with the graph of f(x)=2x and shift it _____________...
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Transcribed Image Text:Let X denote the amount of space occupied by an article placed in a 1-ft3 packing container. The pdf of X is below.
f(x) = {72x7(1-x)
0 < x < 1
otherwise
(a) Graph the pdf.
f(x)
4
3
2
1
f(x)
3
2
Obtain the cdf of X.
0.2
0.2
0.4
0.4
0.6
0.6
0
x < 0
7060 - 01²-6²) ****
F(x) =
9x
-8x
0 x 1
1
X> 1
0.8
0.8
1.0
1.0
X
X
f(x)
4
3
2
1
f(x)
4
3
2
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
1.0
1.0
X
X
![0.8
0.6
0.4
0.2
E(X)=
0.2
0.4
0.6
0.8
X
= 0
x= 0.1208
1.0
What is P(0.45 ≤ x ≤ 0.7)? (Round your answer to four decimal places.)
0
x
0.8
(b) What is P(X ≤ 0.7) [i.e., F(0.7)]? (Round your nswer to four decimal places.)
0.1960
(e) Compute E(X) and (Round your answers to four decimal places.)
ох
X
0.6
0.4
0.2
(c) Using the cdf from (a), what is P(0.45 < X < 0.7)? (Round your answer to four decimal places.)
0.1869
0.2
(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)
0.4
0.6
0.8
1.0
X
(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)
0.1558
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F233b872c-1fd3-4c35-adee-53b885ebb243%2F5965c77c-2b7b-4e55-a495-bc8dfc0583d9%2Fgw1kzro_processed.png&w=3840&q=75)
Transcribed Image Text:0.8
0.6
0.4
0.2
E(X)=
0.2
0.4
0.6
0.8
X
= 0
x= 0.1208
1.0
What is P(0.45 ≤ x ≤ 0.7)? (Round your answer to four decimal places.)
0
x
0.8
(b) What is P(X ≤ 0.7) [i.e., F(0.7)]? (Round your nswer to four decimal places.)
0.1960
(e) Compute E(X) and (Round your answers to four decimal places.)
ох
X
0.6
0.4
0.2
(c) Using the cdf from (a), what is P(0.45 < X < 0.7)? (Round your answer to four decimal places.)
0.1869
0.2
(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)
0.4
0.6
0.8
1.0
X
(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)
0.1558
X
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