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? *

Answer 1

standard deviation = $472.97

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