The mean value of land and buildings per acre from a sample of farms is $1800, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 72. .... (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1700 and $1900, farms (Round to the nearest whole number as needed.)
The mean value of land and buildings per acre from a sample of farms is $1800, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 72. .... (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1700 and $1900, farms (Round to the nearest whole number as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Question:**
The mean value of land and buildings per acre from a sample of farms is $1800, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 72.
(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1700 and $1900.
[ ] farms (Round to the nearest whole number as needed.)
---
**Explanation:**
The empirical rule, also known as the 68-95-99.7 rule, is used in statistics to describe the distribution of data in a normal distribution:
- 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.
For this problem, you need to determine the percentage of farms whose values are within $1700 and $1900, which is one standard deviation ($1800 ± $100) from the mean.
Using the empirical rule, around 68% of the farms should fall within this range. Therefore, approximately 68% of 72 farms can be calculated to estimate the number of farms.
Steps:
1. Calculate 68% of 72 farms:
\[
0.68 \times 72 = 48.96
\]
2. Round to the nearest whole number:
- Approximately 49 farms.
Therefore, approximately 49 farms have land and building values per acre between $1700 and $1900.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faba0b9cd-c878-4f87-bc49-1bf6b97748a3%2F8748677a-d597-4f59-aaf9-076efb821068%2Fi3r5a8b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
The mean value of land and buildings per acre from a sample of farms is $1800, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 72.
(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1700 and $1900.
[ ] farms (Round to the nearest whole number as needed.)
---
**Explanation:**
The empirical rule, also known as the 68-95-99.7 rule, is used in statistics to describe the distribution of data in a normal distribution:
- 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.
For this problem, you need to determine the percentage of farms whose values are within $1700 and $1900, which is one standard deviation ($1800 ± $100) from the mean.
Using the empirical rule, around 68% of the farms should fall within this range. Therefore, approximately 68% of 72 farms can be calculated to estimate the number of farms.
Steps:
1. Calculate 68% of 72 farms:
\[
0.68 \times 72 = 48.96
\]
2. Round to the nearest whole number:
- Approximately 49 farms.
Therefore, approximately 49 farms have land and building values per acre between $1700 and $1900.
Expert Solution
Step 1
By using emperical rule of normal distribution.
Mean = $ 1800
S. D = $ 100
Sample size = 72
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