Important Theorems for Your Reference Chebyshev's Theorem: In any distribution, the portion of data measurements lying within & standard deviations of the mean is at least 1 - No useful information is provided on the proportion (percent) of data that falls within one standard deviation of the mean. At least = (or 75%) of data measurements will fall within two standard deviations of the mean. At least - (or 88.89%) of data measurements will fall within three standard deviations of the mean. At least - (or 93.75%) of data measurements will fall within four standard deviations of the mean The Empirical Rule: In a bell-shaped (normal) distribution, the portion of data measurements will be as follows: Approximately 68% of data measurements fall within one standard deviation of the mean. Approximately 95% of data measurements will fall within two standard deviations of the mean. Approximately 99.7% of data measurements will fall within three standard deviations of the mean. 6. The mean value of land and buildings per acre from a sample of farms in a certain area is $2400 with a standard deviation of $450. Show calculations to support your answer. If it is not possible to determine the answer, explain why. a. Estimate, if possible, the percent of farms whose values are between $1950 and $2850 per acre. b. Estimate, if possible, the percent of farms whose values are between $1050 and $3750 per acre. c. Estimate, if possible, the percent of farms whose values are below $1050 per acre. d. Find the z-score for a farm in this area valued at $1910 per acre. Round to the nearest hundredth Would a farm of this value considered unusual in this area