Questions: The mean value of land and buildings per acre from a sample of farms is 1700, with a standard deviation of 300. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? 1355 2449 1308 563 2069 1804 E. 2449 F. 1308 Which of the farms are very unusual (more than three standard deviations from the mean)? Select all that apply. A. 1804 B. 1308 C. 2449 D. 563 E. 2069 F. 1355 G. None of the data values are very unusual.

The mean value of land and buildings per acre from a sample of farms is 1700, with a standard deviation of 300. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? 1355 2449 1308 563 2069 1804 E. 2449 F. 1308 Which of the farms are very unusual (more than three standard deviations from the mean)? Select all that apply. A. 1804 B. 1308 C. 2449 D. 563 E. 2069 F. 1355 G. None of the data values are very unusual.
Transcript text: Alex Sturgis 2.4 Measure of Variation Question 4, 2.4.33 HW Score: $17.65 \%, 3$ of 17 points Part 2 of 2 Points: 0 of 1 Save The mean value of land and buildings per acre from a sample of farms is $\$ 1700$, with a standard deviation of $\$ 300$. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? \$1355 \$2449 \$1308 \$563 \$2069 \$1804 E. $\$ 2449$ F. $\$ 1308$ Which of the farms are very unusual (more than three standard deviations from the mean)? Select all that apply. A. $\$ 1804$ B. $\$ 1308$ C. $\$ 2449$ D. $\$ 563$ E. $\$ 2069$ F. $\$ 1355$ G. None of the data values are very unusual.
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Solution

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Solution Steps

Step 1: Calculate the Bounds for Unusual and Very Unusual Data Points

Using the formulas:

  • Unusual lower bound: \(\mu - 2\sigma = 1700 - 2 \times 300 = 1100\)
  • Unusual upper bound: \(\mu + 2\sigma = 1700 + 2 \times 300 = 2300\)
  • Very unusual lower bound: \(\mu - 3\sigma = 1700 - 3 \times 300 = 800\)
  • Very unusual upper bound: \(\mu + 3\sigma = 1700 + 3 \times 300 = 2600\)
Step 2: Classify the Data Points

Data points classified as unusual:

  • 2449 Data points classified as very unusual:
  • 563

Final Answer:

Unusual data points: 2449 Very unusual data points: 563

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