Question 1 A & out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. Assume the components function independently of one another. a) In a 3 out of 5 system, each component has probability 0.9 of functioning. What is the probability that the system will function? b) In a 3 out of n system, in which each component has probability of 0.9 of functioning, what is the smallest value of n needed so that the probability that the system functions is at least 0.9? c) In a manufacturing plant, the probability of making a defective bolt 0.1. Estimate the mean and standard deviation of defective bolts in a total of 900 bolts. d) If probability density functions of a random variable x is for-1≤x≤1 f(x) = {8² for any other value of x Find the percentage probability Psxs;})

Question 1 A & out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. Assume the components function independently of one another. a) In a 3 out of 5 system, each component has probability 0.9 of functioning. What is the probability that the system will function? b) In a 3 out of n system, in which each component has probability of 0.9 of functioning, what is the smallest value of n needed so that the probability that the system functions is at least 0.9? c) In a manufacturing plant, the probability of making a defective bolt 0.1. Estimate the mean and standard deviation of defective bolts in a total of 900 bolts. d) If probability density functions of a random variable x is for-1≤x≤1 f(x) = {8² for any other value of x Find the percentage probability Psxs;})

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 16E: Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000...

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