ime261a7s - IME 2610 Fall 2010 Assignment 7 SOLUTIONS Problem 8.4 p 374 = 100 hrs n = 64 x-bar = 350 hrs a 95 Confidence Interval on the Mean <3pts>

# ime261a7s - IME 2610 Fall 2010 Assignment 7 SOLUTIONS...

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IME 2610 Fall 2010 Assignment 7 SOLUTIONS Problem 8.4 p 374 σ= 100 hrs n = 64 x-bar = 350 hrs α=0.05 α/2 = 0.025 a) 95% Confidence Interval on the Mean <3pts> 350 ± 1.96(100/ 64) 325.5 < μ < 374.5 We are 95 % confident mean bulb life is between 325.5 and 374.5 hours. b) <2pts> No, the manufacturer does not have the right to say the mean bulb life is 400. 400 hours is outside of our confidence interval and the probability the mean is greater than 374 .5 is α/2 or 0.025. c) <2pts> No the light-bulb life population life does not have to be normally distributed because we know σ and n = 100, so based on the central limit theorem the sampling distribution of is normally distributed. d) <2pts> An individual value of 320 would be less than one standard deviation away from the sample mean so it would not be considered unusual. A value of 320 does fall outside of the confidence interval but the confidence interval represents bounds on the mean not an individual value. e) <5 pts> σ= 80hrs n = 64 x-bar = 350 hrs α=0.05 α/2 = 0.025 95% Confidence Interval on the Mean 350 ± 1.96(80/ 64) 330.4 < μ < 369.6 We are 95 % confident mean bulb life is between 330.4 and 369.6 hours.