Refer to earlier exercise. The Sylvania CFL 65-watt replacement bulbs that utilise only 16 watts are advertised as having an average lifespan of 8000 hours on their packaging. Assume that the average lifespan of each of these bulbs is 8000 hours, with a 400-hour standard deviation. Determine the likelihood that a random sample of 25 of these bulbs will have a mean life of a. less than 7890 hours b. between 7850 and 7910 hours c. within 130 hours of the population mean d. less than the population mean by 150 hours or more


Answered 1 year ago
Answered 1 year ago
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Recall that for the sampling distribution of xˉ\bar{x}, in an earlier exercise we established the following:

  • the sampling distribution of xˉ\bar{x} is normal

  • μxˉ=8000 hours \mu_{\bar{x}}=8000\text{ hours }

  • σxˉ=40025=80 hours \displaystyle \sigma_{\bar x}=\frac{400}{\sqrt{25}}=80 \text{ hours }

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