Answer:
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.
Answer: 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%
