1. An electrical firm manufactures light bulbs that have a length of life that i
ID: 3304801 • Letter: 1
Question
1. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. A sample of 30 bulbs has an average life of 780 hours. (a) Find the 96% two-sided confidence interval for , the population mean of all bulbs produced by this firm (b) Find an upper 95% bound for . (c) Construct a 99% lower confidence interval on . (d) If we wish to be 95% confident that our sample mean will be within 10 hours of the true mean, how large a sample is needed?Explanation / Answer
Mean is 780 and sd is 40. Also, N is 30
a) Z for 96% confidence is 1.96
thus confidence interval lower limit is (780-1.96*(40/sqrt(30)))=765.69
Also, upper limit is (780+1.96*(40/sqrt(30)))=794.31
b) z for 95% confidence is 1.645 , thus upper limit is (780+1.645*(40/sqrt(30)))=792.013
c) z for 99% confidence is 2.33 thus lower limit is (780-2.33*(40/sqrt(30)))=762.984
upper limit is (780+2.33*(40/sqrt(30)))=797.016
d) this means that 1.645*40/sqrt(N)=10
thus sqrt(N)=1.645*4, thus N is 43
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