# QZ 5-A - least two years(730 days without trouble P X ≥...

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STAT 400 Fall 2011 Version A Name ANSWERS . Quiz 5 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Suppose the duration of trouble-free operation of a new vacuum cleaner is normally distributed with mean 630 days and standard deviation 100 days. a) (3) If the company wishes to set the warranty period so that only 7.5% of the vacuum cleaners would need repair services while under warranty, how long a warranty must be set? Need x = ? such that P( X < x ) = 0.075. o Find z such that P( Z < z ) = 0.075. The area to the left is 0.075 = Φ ( z ). Using the standard normal table, z = 1.44 . t x = μ + σ z . x = 630 + 100 ( 1.44 ) = 486 days . b) (3) What is the probability that a randomly selected vacuum cleaner will work for at

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Unformatted text preview: least two years (730 days) without trouble? P( X ≥ 730 ) = -≥ 100 3 6 730 Z P = P( Z ≥ 1.00 ) = 1 – Φ ( 1.00 ) = 1 – 0.8413 = 0.1587 . c) (4) A cleaning service purchased (a random sample of) 8 vacuum cleaners. Find the probability that the average duration of trouble-free operation of those 8 vacuum cleaners will be at least two years (730 days). μ = 630, σ = 100, n = 8. Need P( X ≥ 730 ) = ? Since the population we sample from is normal, . n Z X =-σ μ P( X ≥ 730 ) = -≥ 8 100 30 6 30 7 Z P = P( Z ≥ 2.83 ) = 1 – Φ ( 2.83 ) = 1 – 0.9977 = 0.0023 ....
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QZ 5-A - least two years(730 days without trouble P X ≥...

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