Answer to Question #271219 in Statistics and Probability for bree

Question

6. A sample of 100 fluorescent tubes from the short life Tube Company gives a mean length of life of 20.5 hours with a standard deviation of 1.6 hours. Find a 95% confidence interval for the average length of life of those tubes 

Answer 1

$n=100 \\ \bar{x} = 20.5 \\ \sigma = 1.6 \\ ME = Z_{α/2} \frac{\sigma}{\sqrt{n}} \\ ME = 1.96 \times \frac{1.6}{\sqrt{100}} = 0.313 \\ Lower \; limit = \bar{x} -ME \\ = 20.5 -0.313 = 20.187 \\ Upper \; limit = \bar{x} + ME \\ = 20.5 + 0.313 = 20.813$