You take a sample of rents of 182 apartments in San Francisco and find that the mean rent is $4000 per month and the standard deviation is $1000 per month. According to Chebyshev's Theorem, what percentage of the rents in your sample fall between $1000 and $7000 per month? At least 89%

89%

Explanation:

according to Chebyshev's theorem, for any k > 1, at least [1 - (1/k^2)] of the data will lie within k standard deviations of the mean.Therefore, Chebyshev's theorem formula can be given as follows:

Chebyshev's theorem formula =  1 - (1/k^2) (1)

In order to fing k, we proceed as follows:

1. Subtract the mean of rents from the larger rent value,

That is, $7,000 - $4,000 = $3,000

2. Divide the difference of $3,000 above by the standard deviation to obtain k as follows:

k = $3,000 ÷ $1000 = 3

3. Substitute 3 for k in equation (1) as follows:

Chebyshev's theorem formula =  1 - (1/3^2)

                                                   = 1 - (1/9)

                                                    = 1 - 0.11

                                                    = 0.89

If we multiply 0.89 by 100, we have 89%.

Therefore, 89% of the rents in the sample will fall between $1000 and $7000 per month.

Between $2,000 and $6,000

Explanation:

The probability must be between $2,000 and $6,000, that is, k=3, the standard deviation of the mean.

∴ 1 - 1/k²=  1 - 1/3² = 9 - 1/9 = 8/9

Hence, 8/9 of 100% = 89%

The probability between $2,000 and $6,000 must be at least 89%

if you use only 25 for your entertainment and only 200 for the groceries that you really need and take out the 50 per month for the computer then that should be enough