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# QZ 5-D - are replaced after how many hours should all the...

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STAT 400 Fall 2011 Version D 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 2,000 hours and standard deviation of 300 hours. a) (3) What is the probability that a bulb would last over 2,180 hours? P( X > 2,180 ) = - > 300 000 2 180 2 Z P , , = P( Z > 0.60 ) = 1 – Φ ( 0.60 ) = 1 – 0.7257 = 0.2743 . b) (3) If the department wants no more than 9% of the bulbs to burn out before they

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Unformatted text preview: are replaced, after how many hours should all the bulbs be replaced? 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 ). z = – 1.34 . t x = μ + σ ⋅ z . x = 2,000 + 300 ⋅ ( – 1.34 ) = 1,598 hours . c) (4) What is the probability that the average lifetime of six randomly and independently selected bulbs is over 2,180 hours? Since the distribution we sample from is normal (Case 2), . n Z X =-σ μ . P ( X > 2,180 ) = -> 6 300 000 , 2 180 , 2 Z P = P ( Z > 1.47 ) = 1 – Φ ( 1.47 ) = 0.0708 ....
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QZ 5-D - are replaced after how many hours should all the...

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