320_hw7 - Economics 320: Homework 7 Continuous...

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Economics 320: Homework 7 Continuous Distributions: Exponential Sampling Distributions EXPONENTIAL DISTRIBUTION: 1. Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.1 claims per month. a. What is the probability that the dealership will wait at least 6 months until the next claim? b. At least a year? c. At least 6 months but not more than 1 year? 2. In 1982, the in-flight shutdown rate for the Garrett TFE731 turbofan engine was 6.0 shutdowns per 100,000 hours. In 1992, with improvements, the in-flight shutdown rate for this same engine dropped to 1.5 shutdowns per 100,000 hours. a. Find the probability that at least 50,000 hours would elapse before the next in- flight shutdown in 1982. b. Calculate the same probability in 1992. c. How would you characterize the degree of improvement? SAMPLING DISTRIBUTIONS: 3. Suppose the probability distribution of X is given by x P(x) 1 | 0.3 2 | 0.1 3 | 0.6 a. Draw a sample of size three from this population and assume x
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