Posted by **David** on Tuesday, June 11, 2013 at 1:44pm.

1. The mean monthly mortgage paid by all home owners in a town is $2365 with a standard deviation of $340. a) Using Chebyshev’s theorem, find at least what percentage of all home owners in this town pay a monthly mortgage of (i) $1685 to $3045 & (ii) $1345 to $3385

b) Using Chebyshev’s theorem, find the interval that contains the monthly mortgage payments of at least 84% of all home owners in this town.

- Statistics -
**MathGuru**, Tuesday, June 11, 2013 at 6:59pm
Chebyshev's theorem says:

1. Within two standard deviations of the mean, you will find at least 75% of the data.

2. Within three standard deviations of the mean, you will find at least 89% of the data.

Part (i) is within two standard deviations of the mean.

Part (ii) is within three standard deviations of the mean.

- Statistics -
**MathGuru**, Tuesday, June 11, 2013 at 7:06pm
There is a formula you can use to find part b).

1 - (1/k^2) = .84 (or 84%)

k = 2.5 (standard deviations)

Therefore, find the amounts within 2.5 standard deviations of the mean. Remember that one standard deviation is equal to $340.

I'll let you take it from here.

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