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29 May, 16:37

A random sample of 42 textbooks has a mean price of $114.50 and a standard deviation of $12.30.

Find a 98% confidence interval for the mean price of all textbooks.

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  1. 29 May, 17:05
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    Step-by-step explanation:

    We want to determine a 98% confidence interval for the mean price for textbooks.

    Number of sample, n = 42

    Mean, u = $114.5

    Standard deviation, s = $12.3

    For a confidence level of 98%, the corresponding z value is 2.33.

    We will apply the formula

    Confidence interval

    = mean ± z * standard deviation/√n

    It becomes

    114.5 ± 2.33 * 12.3/√42

    = 114.5 ± 2.33 * 1.898

    = 114.5 ± 4.42

    The lower end of the confidence interval is 114.5 - 4.42 = 110.08

    The upper end of the confidence interval is 114.5 + 4.42 = 118.92

    Therefore, with 98% confidence interval, the mean price of all textbooks is between $110.08 and $118.92
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