# QZ 5-B - under warranty how long a warranty must be set...

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STAT 400 Fall 2011 Version B 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 particular brand of a FAX machine is approximately normally distributed with mean 410 days and standard deviation 60 days. a) (3) What is the probability that a FAX machine of this brand will work for over 1 year (365 days) without trouble? P( X 365 ) = - 60 410 365 Z P = P( Z 0.75 ) = 1 – Φ ( 0.75 ) = 1 – 0.2266 = 0.7734 . b) (3) If the company that makes this particular brand of a FAX machine wishes to set the warranty period so that only 9% of all FAX machines would need repair services while
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Unformatted text preview: under warranty, how long a warranty must be set? Need x = ? such that P( X < x ) = 0.09. o Find z such that P( Z < z ) = 0.09. The area to the left is 0.09 = Φ ( z ). Using the standard normal table, z = – 1.34 . t x = μ + σ ⋅ z . x = 410 + 60 ⋅ ( – 1.34 ) = 329.6 days . d) (4) What is the probability that the average duration of trouble-free operation of (a random sample of) 10 FAX machines is over 1 year (365 days)? μ = 410, σ = 60, n = 10. Need P( X ≥ 365 ) = ? Since the population we sample from is normal, . n Z X =-σ μ P( X ≥ 365 ) = -≥ 10 60 410 365 Z P = P( Z ≥ – 2.37 ) = 1 – Φ ( – 2.37 ) = 1 – 0.0089 = 0.9911 ....
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