### Exploring the Age Distribution of Home Buyers: An Application of Chebyshev's TheoremA real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 45 years old, with a standard deviation of 11 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.1. According to Chebyshev's theorem, at least 56% of the home buyers' ages lie between [ ] years and [ ] years. (Round your answer to the nearest whole number.) 2. According to Chebyshev's theorem, at least (Choose one) of the home buyers' ages lie between 23 years and 67 years.#### Details on the use of Chebyshev's Theorem:Chebyshev's theorem provides a way to determine the minimum proportion of values that lie within a certain number of standard deviations from the mean in any dataset, regardless of how the data is distributed. The theorem states:\[ \text{Proportion} \geq 1 - \frac{1}{k^2} \]where $ k $ is the number of standard deviations from the mean.In this example, apply the theorem to learn more about the age distribution of home buyers. #### Example Calculations:- For question (a), determine the range of ages that contains at least 56% of the data using Chebyshev's inequality.- For question (b), select the appropriate percentage to describe the distribution of ages between 23 and 67 years.By understanding these calculations, you can better grasp the dispersion and variability in the age of home buyers based on the given mean and standard deviation.

The Chebychev's inequality is generally used for data with high variation. It does not makes any…

A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 45 years old, with a standard deviation of 11 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers. (a) According to Chebyshev's theorem, at least 56% of the home buyers' ages lie between years and years. (Round your answer to the nearest whole number.) (b) According to Chebyshev's theorem, at least (Choose one) of the home buyers' ages lie between 23 years and 67 years.

A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 45 years old, with a standard deviation of 11 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers. (a) According to Chebyshev's theorem, at least 56% of the home buyers' ages lie between years and years. (Round your answer to the nearest whole number.) (b) According to Chebyshev's theorem, at least (Choose one) of the home buyers' ages lie between 23 years and 67 years.

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### Exploring the Age Distribution of Home Buyers: An Application of Chebyshev's Theorem

A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 45 years old, with a standard deviation of 11 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.

1. According to Chebyshev's theorem, at least 56% of the home buyers' ages lie between [ ] years and [ ] years. (Round your answer to the nearest whole number.)

2. According to Chebyshev's theorem, at least (Choose one) of the home buyers' ages lie between 23 years and 67 years.

#### Details on the use of Chebyshev's Theorem:

Chebyshev's theorem provides a way to determine the minimum proportion of values that lie within a certain number of standard deviations from the mean in any dataset, regardless of how the data is distributed. The theorem states:

\[ \text{Proportion} \geq 1 - \frac{1}{k^2} \]

where $ k $ is the number of standard deviations from the mean.

In this example, apply the theorem to learn more about the age distribution of home buyers.

#### Example Calculations:

- For question (a), determine the range of ages that contains at least 56% of the data using Chebyshev's inequality.
- For question (b), select the appropriate percentage to describe the distribution of ages between 23 and 67 years.

By understanding these calculations, you can better grasp the dispersion and variability in the age of home buyers based on the given mean and standard deviation.

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