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QZ 5-C - P Z< z = 0.04 The area to the left is 0.04 = Φ...

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STAT 400 Fall 2011 Version C 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. The maintenance department of a city's electric power company finds that it is cost-efficient to replace all streetlight bulbs at once, rather than replacing the bulbs individually as they burn out. Assume that the lifetime of a bulb is normally distributed, with a mean of 3,000 hours and standard deviation of 200 hours. a) (3) If the department wants no more than 4% of the bulbs to burn out before they are replaced, after how many hours should all the bulbs be replaced? Need x = ? such that P( X < x ) = 0.04. onesans Find z
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Unformatted text preview: P( Z < z ) = 0.04. The area to the left is 0.04 = Φ ( z ). z = – 1.75 . t x = μ + σ ⋅ z . x = 3,000 + 200 ⋅ ( – 1.75 ) = 2,650 hours . b) (3) What is the probability that a bulb would last over 3,150 hours? P( X > 3,150 ) = -> 200 000 , 3 150 , 3 Z P = P( Z > 0.75 ) = 1 – Φ ( 0.75 ) = 1 – 0.7734 = 0.2266 . c) (4) What is the probability that the average lifetime of eight randomly and independently selected bulbs is over 3,150 hours? Since the distribution we sample from is normal (Case 2), . n Z X =-σ μ . P ( X > 3,150 ) = -> 8 200 000 , 3 150 , 3 Z P = P ( Z > 2.12 ) = 1 – Φ ( 2.12 ) = 0.0170 ....
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