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29 September, 01:12

Suppose the number of inches of rainfall each year in a city is normally distributed. For a random sample of years, the confidence interval (3.9,7.7) is generated. Find the margin of error Give just a number for your answer. For example, if you found that the margin of error was 2, you would enter 2.

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  1. 29 September, 05:05
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    Margin of error = 1.9 ≅2

    Step-by-step explanation:

    Given the number of inches of rainfall each year in a city is normally distributed.

    For a random sample of years, the confidence interval (3.9,7.7) is generated

    We know that the confidence intervals of margin of error is defined by

    x⁻ ± margin of error

    x⁻ ± M. E

    Given the confidence intervals are (3.9,7.7)

    Equating lower limit x⁻ - M. E = 3.9 ... (i)

    Equating upper limit x⁻ + M. E = 7.7 ... (ii)

    adding The equations (i) and (ii) and simplification, we get

    2x⁻ = 11.6

    Dividing by '2' on both sides, we get

    x⁻ = 5.8

    This is the mean of the sample x⁻ = 5.8

    now substitute mean value in equation (i)

    x⁻ - M. E = 3.9

    5.8 - Margin of error = 3.9

    Margin of error = 5.8 - 3.9

    Margin of error = 1.9 ≅2

    Conclusion:-

    Margin of error = 1.9 ≅2

    Verification:-

    In given data lower imit x⁻ - M. E = 3.9

    we know that x⁻ = 5.8 and margin of error = 2

    5.8 - 1.9 = 3.9

    3.9=3.9
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