The heights in inches of orangutans Are normally distributed with a population standard deviation of 3″ and an unknown population mean if a

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The heights in inches of orangutans Are normally distributed with a population standard deviation of 3″ and an unknown population mean if a random sample of 17 orangutans is taken and results in a sample mean of 57″ find the error bound of the confidence interval with a 95% confidence level

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Thu Thảo 4 years 2021-08-02T17:32:39+00:00 1 Answers 21 views 0

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  1. Tryphena
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    2021-08-02T17:34:03+00:00
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    Answer: The 95% confidence interval is approximately (55.57, 58.43)

    ======================================================

    Explanation:

    At 95% confidence, the z critical value is about z = 1.960 which you find using a table or a calculator.

    The sample size is n = 17

    The sample mean is xbar = 57

    The population standard deviation is sigma = 3

    The lower bound of the confidence interval is

    L = xbar – z*sigma/sqrt(n)

    L = 57 – 1.960*3/sqrt(17)

    L = 55.5738905247863

    L = 55.57

    The upper bound is

    U = xbar + z*sigma/sqrt(n)

    U = 57 + 1.960*3/sqrt(17)

    U = 58.4261094752137

    U = 58.43

    Therefore the confidence interval (L, U) turns into (55.57, 58.43) which is approximate.

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