QZ 5-A - least two years (730 days) without trouble? P( X...

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 A 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 new vacuum cleaner is normally distributed with mean 630 days and standard deviation 100 days. a) (3) If the company wishes to set the warranty period so that only 7.5% of the vacuum cleaners would need repair services while under warranty, how long a warranty must be set? Need x = ? such that P( X < x ) = 0.075. o Find z such that P( Z < z ) = 0.075. The area to the left is 0.075 = Φ ( z ). Using the standard normal table, z = 1.44 . t x = μ + σ z . x = 630 + 100 ( 1.44 ) = 486 days . b) (3) What is the probability that a randomly selected vacuum cleaner will work for at
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: least two years (730 days) without trouble? P( X 730 ) = - 100 3 6 730 Z P = P( Z 1.00 ) = 1 ( 1.00 ) = 1 0.8413 = 0.1587 . c) (4) A cleaning service purchased (a random sample of) 8 vacuum cleaners. Find the probability that the average duration of trouble-free operation of those 8 vacuum cleaners will be at least two years (730 days). = 630, = 100, n = 8. Need P( X 730 ) = ? Since the population we sample from is normal, . n Z X =- P( X 730 ) = - 8 100 30 6 30 7 Z P = P( Z 2.83 ) = 1 ( 2.83 ) = 1 0.9977 = 0.0023 ....
View Full Document

Page1 / 2

QZ 5-A - least two years (730 days) without trouble? P( X...

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