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7 June, 18:02

A federal bank examiner is interested in estimating the mean outstanding defaulted loans balance of all defaulted loans over the last three years. A random sample of 10 defaulted loans yielded a mean of $60,850 with a standard deviation of $16,100.22. Calculate a 90 percent confidence interval for the mean balance of defaulted loans over the past three years.

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  1. 7 June, 20:25
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    Answer: = ($52,474.75, $69,225.25)

    Therefore at 90% confidence interval = ($52,474.75, $69,225.25)

    Step-by-step explanation:

    Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

    The confidence interval of a statistical data can be written as.

    x+/-zr/√n

    Given that;

    Mean x = $60,850

    Standard deviation r = $16,100.22

    Number of samples n = 10

    Confidence interval = 90%

    z (at 90% confidence) = 1.645

    Substituting the values we have;

    60,850+/-1.645 (16,100.22/√10)

    60,850+/-1.645 (5091.336602979)

    60,850+/-8375.248711901

    $60,850+/-8375.248711901+ / - $8375.25

    = ($52474.75, $69225.25)

    Therefore at 90% confidence interval = ($52474.75, $69225.25)
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