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Exercise 5.3 An electronic scale at an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.01 and fills are independent. 1. Determine the probability mass function of the number of fills (X) before the manufacturing line is stopped. 2. Find the probability that at least 100 fills can be completed before the manufacturing line is stopped. 3. Calculate the mean and variance of X.

Exercise 5.3 An electronic scale at an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.01 and fills are independent. 1. Determine the probability mass function of the number of fills (X) before the manufacturing line is stopped. 2. Find the probability that at least 100 fills can be completed before the manufacturing line is stopped. 3. Calculate the mean and variance of 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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Exercise 5.3 An electronic scale at an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.01 and fills are independent. 1. Determine the probability mass function of the number of fills (X) before the manufacturing line is stopped. 2. Find the probability that at least 100 fills can be completed before the manufacturing line is stopped. 3. Calculate the mean and variance of X.
Transcribed Image Text:Exercise 5.3 An electronic scale at an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.01 and fills are independent. 1. Determine the probability mass function of the number of fills (X) before the manufacturing line is stopped. 2. Find the probability that at least 100 fills can be completed before the manufacturing line is stopped. 3. Calculate the mean and variance of X.
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