Final answer:
To use Chebyshev's theorem, subtract the mean from the upper and lower bounds of the range, divide by the standard deviation, and use the formula 1 - (1 / standard deviation squared) to find the minimum percentage of data values that will fall within the range of 338-548 acres. In this case, the minimum percentage is 84%.
Step-by-step explanation:
To use Chebyshev's theorem to find the minimum percentage of data values that will fall in the range of 338-548 acres, we need to determine how many standard deviations away from the mean this range is. To do this, we subtract the mean from the upper and lower bounds of the range:
Upper Bound: 548 acres - 443 acres = 105 acres
Lower Bound: 338 acres - 443 acres = -105 acres
Next, we divide the upper and lower bounds by the standard deviation to get the number of standard deviations away from the mean:
Upper Standard Deviation: 105 acres / 42 acres = 2.5
Lower Standard Deviation: -105 acres / 42 acres = -2.5
According to Chebyshev's theorem, at least 1 - (1 / standard deviation squared) of the data will fall within the range of ±2.5 standard deviations from the mean. In this case, at least 1 - (1 / (2.5)^2) = 1 - (1 / 6.25) = 0.84 or 84% of the data values will fall within the range of 338-548 acres.