Homework 4 Solutions

# Homework 4 Solutions - Homework 4 Chapter 7 Problem 2 The...

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Homework 4 Chapter 7 Problem 2 The length of time a system is “down” (that is, broken) is described (approximately) by the probability distribution in Table 7.6.2. Assume that these downtimes are exact. That is, there are three types of easily recognized problems that always take this long (5, 30, or 120 minutes) to fix. Probability Distribution of Downtime Problem Downtime (minutes) Probability Minor 5 0.60 Substantial 30 0.30 Catastrophic 120 0.10 a. What kind of probability distribution does this table represent? This is a discrete random variable. b. Find the mean downtime. Mean downtime = (5 * 0.60) + (30 * 0.30) + (120 * 0.10) = 24 minutes c. Find the standard deviation of the downtime. 9 . 33 ) 10 . 0 ( ) 24 120 ( ) 30 . 0 ( ) 24 30 ( ) 60 . 0 ( ) 24 5 ( 2 2 2 = - + - + - minutes d. What is the probability that the downtime will be greater than 10 minutes, according to this table? The probability is 0.30 + 0.10 = 0.40. e.

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Homework 4 Solutions - Homework 4 Chapter 7 Problem 2 The...

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