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22 July, 01:13

A random sample of 56 fluorescent light bulbs has a mean life of 645 hours. Assume the population standard deviation is 31 hours. Construct a 95% confidence interval for the population mean

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  1. 22 July, 01:32
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    Step-by-step explanation:

    We want to determine a 95% confidence interval for the population mean.

    Number of sample, n = 56

    Mean, u = 645 hours

    Standard deviation, s = 31 hours

    For a confidence level of 95%, the corresponding z value is 1.96.

    We will apply the formula

    Confidence interval

    = mean ± z * standard deviation/√n

    It becomes

    645 ± 1.96 * 31/√56

    = 645 ± 1.96 * 4.142

    = 645 ± 8.12

    The lower end of the confidence interval is 645 - 8.12 = 636.88

    The upper end of the confidence interval is 645 + 8.12 = 653.12

    Therefore, with 95% confidence interval for the population mean life of fluorescent light bulbs is between 636.88 hours and 653.12 hours
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