A home security system is designed to have 99% reliability rate. Suppose that nine homes equipped with this system experienced an attempted burglary. a) Find the formula for the probability distribution of X representing the number of alarms that triggered during an attempted burglary. b) Calculate the mean and standard deviation of X. c) Find the probability that at least one of the alarms is triggered.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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A home security system is designed to have 99% reliability rate. Suppose that nine homes
equipped with this system experienced an attempted burglary.
a) Find the formula for the probability distribution of X representing the number of
alarms that triggered during an attempted burglary.
b) Calculate the mean and standard deviation of X.
c) Find the probability that at least one of the alarms is triggered.
d) Find the probability that more than seven of the alarms are triggered.
Transcribed Image Text:A home security system is designed to have 99% reliability rate. Suppose that nine homes equipped with this system experienced an attempted burglary. a) Find the formula for the probability distribution of X representing the number of alarms that triggered during an attempted burglary. b) Calculate the mean and standard deviation of X. c) Find the probability that at least one of the alarms is triggered. d) Find the probability that more than seven of the alarms are triggered.
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