Home values Assessment records indicate that the value of...

Home values Assessment records indicate that the value of homes in a small city is skewed right, with a mean of $\$ 140,000$ and standard deviation of $\$ 60,000$. To check the accuracy of the assessment data, officials plan to conduct a detailed appraisal of 100 homes selected at random. Using the 68–95–99.7 Rule, draw and label an appropriate sampling model for the mean value of the homes selected.

Key Concepts

Central Limit Theorem

This concept explains that the distribution of the sample mean will tend to be normal (or approximately normal) when the sample size is sufficiently large, regardless of the shape of the original population distribution. It justifies using the normal probability model even when the population is skewed, as long as the sample size is large enough.

Sampling Distribution of the Sample Mean

The sampling distribution of the sample mean is the probability distribution of all possible sample means computed from samples of the same size drawn from the population. It is centered at the population mean and has a spread (standard deviation) that is smaller than the population standard deviation.

Standard Error

This is the standard deviation of the sampling distribution of the sample mean. It quantifies the variability of sample means around the true population mean and is equal to the population standard deviation divided by the square root of the sample size.

68–95–99.7 Rule

Also known as the Empirical Rule, this rule states that for a normal distribution approximately 68% of the data will fall within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations. This rule is used to assess probability and the spread of data in the context of a sampling distribution.

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