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3. Pieces of 2 by 4 by 72 lumber sold by a certain yard have been observed by a consumer watchdog to have 0, 1, 2, 3, 4, or 5 visible flaws (but rarely more). The probabilities for various numbers of flaws are provided by its cumulative distribution function F(x) = P(X≤x): 0 1 2 3 4 X F(x) .45 .67 .81 .89 .96 a) As a customer, I find it unacceptable to buy such a piece of lumber if it has more than 3 flaws. What is the probability that a piece I buy will by accident be unacceptable? b) Find the average number of flaws in a piece of lumber chosen arbitrarily, E(X).

3. Pieces of 2 by 4 by 72 lumber sold by a certain yard have been observed by a consumer watchdog to have 0, 1, 2, 3, 4, or 5 visible flaws (but rarely more). The probabilities for various numbers of flaws are provided by its cumulative distribution function F(x) = P(X≤x): 0 1 2 3 4 X F(x) .45 .67 .81 .89 .96 a) As a customer, I find it unacceptable to buy such a piece of lumber if it has more than 3 flaws. What is the probability that a piece I buy will by accident be unacceptable? b) Find the average number of flaws in a piece of lumber chosen arbitrarily, E(X).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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3. Pieces of 2 by 4 by 72 lumber sold by a certain yard have been observed by a consumer watchdog to have 0, 1, 2, 3, 4, or 5 visible flaws (but rarely more). The probabilities for various numbers of flaws are provided by its cumulative distribution function F(x) = P(X≤x): 0 1 2 3 4 X F(x) .45 .67 .81 .89 .96 a) As a customer, I find it unacceptable to buy such a piece of lumber if it has more than 3 flaws. What is the probability that a piece I buy will by accident be unacceptable? b) Find the average number of flaws in a piece of lumber chosen arbitrarily, E(X).
Transcribed Image Text:3. Pieces of 2 by 4 by 72 lumber sold by a certain yard have been observed by a consumer watchdog to have 0, 1, 2, 3, 4, or 5 visible flaws (but rarely more). The probabilities for various numbers of flaws are provided by its cumulative distribution function F(x) = P(X≤x): 0 1 2 3 4 X F(x) .45 .67 .81 .89 .96 a) As a customer, I find it unacceptable to buy such a piece of lumber if it has more than 3 flaws. What is the probability that a piece I buy will by accident be unacceptable? b) Find the average number of flaws in a piece of lumber chosen arbitrarily, E(X).
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