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 troublefree 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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This note was uploaded on 02/15/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Statistics, Probability

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