320_hw7_ans

320_hw7_ans
Download Document
Showing pages : 1 - 2 of 3
This preview has blurred sections. Sign up to view the full version! View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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? i. λ is the mean number of occurrences per time unit ; so λ = 0.1 ii. F(x) = 1 - x e λ-for x > 0. iii. P(x > 6) = x e-= 6 * 1 .-e = 0.5488 b. At least a year? i. P(x > 12) = x e-= 12 * 1 .-e = 0.3012 c. At least 6 months but not more than 1 year? i. P(6 < x < 12) = (1 - 12 * 1 .-e ) - (1 - 6 * 1 .-e ) = 0.2476 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. i. λ is the mean number of occurrences per time unit ; so λ(1982) = 6 and λ(1992) = 1.5 ii. for 1982: P(x > ½) = 5 . * 6-e = 0.0498 b. Calculate the same probability in 1992. ...
View Full Document