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To determine p, the proportion of time that an airline

Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani ISBN: 9780131453401 223

Solution for problem 13 Chapter 11.3

Fundamentals of Probability, with Stochastic Processes | 3rd Edition

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Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani

Fundamentals of Probability, with Stochastic Processes | 3rd Edition

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Problem 13

To determine p, the proportion of time that an airline operator is busy answering customers, a supervisor observes the operator at times selected randomly and independently from other observed times. Let Xi = 1 if the ith time the operator is observed, he is busy; let Xi = 0 otherwise. For large values of n, if (1/n)/n i=1 Xis are taken as estimates of p, for what values of n is the error of estimation at most 0.05 with probability 0.96?

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Statistical Inference: provides methods for drawing conclusions about a population from the sample data. There are two ways to do this:  Confidence intervals: used to estimate the value of a population parameter using sample statistics Test of Significance: used for assessing evidence for a claim about the  population To set up  Have to have an SRS from the population, no bias  The variable has to have an exactly normal distribution in the population  We don’t know population mean , but we know the population standard deviation Confidence Interval  What statistic can be used to estimate the population parameter o We can use x-bar  To do a confidence interval, it is similar to the 68-95-99.7

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Chapter 11.3, Problem 13 is Solved
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Textbook: Fundamentals of Probability, with Stochastic Processes
Edition: 3
Author: Saeed Ghahramani
ISBN: 9780131453401

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To determine p, the proportion of time that an airline