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Unformatted text preview: UNIVERSITY OF CALIFORNIA, LOS ANGELES
Civil and Environmental Engineering Department
CEE 110 Introduction to Probability and Statistics for Engineers
Spring Quarter 2011
MW 122 PM
Franz 1178 Prof. K. D. Stolzenbach
5732J Boelter Hall, 2067624
stolzenb@ucla.edu Problem Set 5 Solutions
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1. a) 95% Twosided CI on the true mean life of a 75watt light bulb
For α = 0.05, zα/2 = z0.025 = 1.96 , and x = 1014, σ =25 , n=20 b) 95% Onesided CI on the true mean piston ring diameter
For α = 0.05, zα = z0.05 =1.65 and x = 1014, σ =25 , n=20 The lower bound of the one sided confidence interval is higher than the lower bound of the
twosided confidence interval even though the level of significance is the same. This is
because all of the Type I probability (or α) is in the left tail (or in the lower bound). 2. 95% Confident that the error of estimating the true mean life of a 75watt light bulb is less
than 5 hours.
For α = 0.05, zα/2 = z0.025 = 1.96 , and σ =25 , E=5 Always round up to the next number, therefore n = 97 3. 99% lower confidence bound on mean Izod impact strength 4. 90% CI on the mean frequency of a beam subjected to loads 5. a) 95% Confidence Interval on the death rate from lung cancer. b) E = 0.03, α = 0.05, zα/2 = z0.025 = 1.96 and = 0.823 as the initial estimate of p,
, n ≅ 622.
c) E = 0.03, α = 0.05, zα/2 = z0.025 = 1.96 at least 95% confident
,
n ≅ 1068. 6. a) 95% Confidence Interval on the true proportion of helmets showing damage b) c) 7. ...
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This note was uploaded on 10/22/2011 for the course ENG 101 taught by Professor Yukov during the Spring '11 term at UCLA.
 Spring '11
 Yukov
 Environmental Engineering

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