HW 6 Solutions

# HW 6 Solutions - Steven Weber Dept of ECE Drexel University...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010) Homework 6 Solutions Question 1: Exercise 55, § 3.4, p.114 Twenty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 60% can be repaired, whereas the other 40% must be replaced with a new unit. If a company purchases ten of these telephones, what is the probability that exactly two will end up being replaced under warranty? The probability of a phone needing repair and being replaced under warranty is: P (repair replaced) = P (replaced | repair) P (repair) = 0 . 4 × 0 . 2 = 0 . 08 . (1) Let X Bin(10 , 0 . 08) be the binomial random variable giving the number of the 10 purchased phones needing repair that require replacement. The problem asks for P ( X = 2). P ( X = 2) = 10 2 0 . 08 2 × 0 . 92 8 0 . 1478 . (2) Question 2: Exercise 60, § 3.4, p.115 A toll bridge charges \$ 1.00 for passenger cars and \$ 2.50 for other vehicles. Suppose that during daytime hours, 60% of all vehicles are passenger cars. If 25 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue?

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