11-2. Let X ( the length of life in hours of a certain brand of 100-watt frosted...

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11-2. Let X ( the length of life in hours of a certain brand of 100-watt frosted light bulb) be N(μ, 500). A random sample of n = 20 bulbs was tested

(until they all burned out), yielding a mean life of ¯x = 1357 hours. Find a 95% confidence interval for μ. Explain your result. Suppose X is not assumed to be normal but we have σ = 500. Can we still find a 95%

confidence interval for μ? What if we increase n to 150 and find ¯x = 1400 and s = 5.57? What are the new 95% confidence limits. What theorem legitimizes them?

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Muhammad Salman Alvi

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