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The mean value of land and buildings per acre from a sample of farms is $1700, with a standard deviation of $200. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 71. (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1300 and $2100. farms (Round to the nearest whole number as needed.)

The mean value of land and buildings per acre from a sample of farms is $1700, with a standard deviation of $200. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 71. (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1300 and $2100. farms (Round to the nearest whole number as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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**Title: Estimating Farm Values Using Statistical Methods** --- **The Mean Value of Farm Land and Buildings:** The mean value of land and buildings per acre from a sample of farms is $1700, with a standard deviation of $200. The data set has a bell-shaped (normal) distribution. Assume the number of farms in the sample is 71. --- **Applying the Empirical Rule:** To estimate the number of farms whose land and building values per acre are between $1300 and $2100, we can use the empirical rule (also known as the 68-95-99.7 rule). This rule states: - Approximately 68% of the data falls within one standard deviation of the mean. - Approximately 95% of the data falls within two standard deviations of the mean. - Approximately 99.7% of the data falls within three standard deviations of the mean. Given: - Mean (μ) = $1700 - Standard Deviation (σ) = $200 **Calculations:** 1. Calculate the range within one standard deviation from the mean: - Lower Bound: μ - σ = $1700 - $200 = $1500 - Upper Bound: μ + σ = $1700 + $200 = $1900 2. Calculate the range within two standard deviations from the mean: - Lower Bound: μ - 2σ = $1700 - $400 = $1300 - Upper Bound: μ + 2σ = $1700 + $400 = $2100 **Interpretation:** Using the empirical rule, we estimate that approximately 95% of the farms have land and building values per acre between $1300 and $2100. --- **Exercise:** (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1300 and $2100. Answer: (Round to the nearest whole number as needed.) - **Estimated Number of Farms = 0.95 * 71 ≈ 67.45 ≈ 67 farms** This means around 67 out of the 71 farms are expected to have land and building values per acre between $1300 and $2100. --- (Note: The empirical rule is a useful tool in statistics for understanding the distribution of data in a normal distribution.)
Transcribed Image Text:**Title: Estimating Farm Values Using Statistical Methods** --- **The Mean Value of Farm Land and Buildings:** The mean value of land and buildings per acre from a sample of farms is $1700, with a standard deviation of $200. The data set has a bell-shaped (normal) distribution. Assume the number of farms in the sample is 71. --- **Applying the Empirical Rule:** To estimate the number of farms whose land and building values per acre are between $1300 and $2100, we can use the empirical rule (also known as the 68-95-99.7 rule). This rule states: - Approximately 68% of the data falls within one standard deviation of the mean. - Approximately 95% of the data falls within two standard deviations of the mean. - Approximately 99.7% of the data falls within three standard deviations of the mean. Given: - Mean (μ) = $1700 - Standard Deviation (σ) = $200 **Calculations:** 1. Calculate the range within one standard deviation from the mean: - Lower Bound: μ - σ = $1700 - $200 = $1500 - Upper Bound: μ + σ = $1700 + $200 = $1900 2. Calculate the range within two standard deviations from the mean: - Lower Bound: μ - 2σ = $1700 - $400 = $1300 - Upper Bound: μ + 2σ = $1700 + $400 = $2100 **Interpretation:** Using the empirical rule, we estimate that approximately 95% of the farms have land and building values per acre between $1300 and $2100. --- **Exercise:** (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1300 and $2100. Answer: (Round to the nearest whole number as needed.) - **Estimated Number of Farms = 0.95 * 71 ≈ 67.45 ≈ 67 farms** This means around 67 out of the 71 farms are expected to have land and building values per acre between $1300 and $2100. --- (Note: The empirical rule is a useful tool in statistics for understanding the distribution of data in a normal distribution.)
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