Assuming the average monthly mortgage payment is normally distributed with a mean of $1,437 AND that 97.35% of the mortgages are between $38

Question

Assuming the average monthly mortgage payment is normally distributed with a mean of $1,437 AND that 97.35% of the mortgages are between $387 and $2,137 – what is the standard deviation? *

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1 week 2021-09-08T17:45:46+00:00 1 Answer 0

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    2021-09-08T17:47:37+00:00

    Answer:

    standard deviation = $472.97

    Step-by-step explanation:

    mean $1,437

    97.35% range between $387 and $2,137

    z = (x – μ) / σ

    • μ = 1,437
    • z = since this is a to tailed distribution, we must divide 0.9735 by 2 = 0.48675 or 0.4868. The z score for 0.4868 in a two tail distribution = 2.22
    • x = choose either 387 or 2,137 for x, the difference with μ = 1,050 either way

    2.22 = 1,050 / σ

    σ = 1,050 / 2.22 = $472.97

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