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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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 = ( z ). z = 1.34 . t x = + 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 =- . P ( X > 2,180 ) = -> 6 300 000 , 2 180 , 2 Z P = P ( Z > 1.47 ) = 1 ( 1.47 ) = 0.0708 ....
View Full Document

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online