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23 August, 08:52

The amount of material used in making a custom sail for a sailboat is normally distributed with a standard deviation of 64 square feet. For a random sample of 15 sails, the mean amount of material used is 912 square feet. Which of the following represents a 99% confidence interval for the population mean amount of material used in a custom sail? A. 912 ± 49.2B. 912 ± 46.8C. 912 ± 42.6D. 912 ± 44.3

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  1. 23 August, 12:38
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    option (B) 912 ± 42.6

    Explanation:

    Data provided in the question:

    Standard deviation = 64 square feet

    Sample size, n = 15

    Mean = 912

    Confidence level = 99%

    Now,

    Confidence interval = Mean ± z[s : √n]

    here,

    z = 2.58 for 99% confidence level

    Thus,

    Confidence interval = 912 ± 2.58[64 : √15]

    or

    Confidence interval = 912 ± 2.58[64 : √15]

    or

    Confidence interval = 912 ± [ 2.58 * 16.525 ]

    or

    Confidence interval = 912 ± 42.63

    = 912 ± 42.6

    Hence,

    The answer is option (B) 912 ± 42.6
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