Use the Empirical Rule. Use the sample statistics from...

Use the Empirical Rule. Use the sample statistics from Exercise 30 and assume the number of households in the sample is $40 .$ (a) Estimate the number of households whose monthly utility bills are between $\$ 54$ and $\$ 86$ (b) In a sample of 20 additional households, about how many households would you expect to have monthly utility bills between $\$ 54$ and $\$ 86 ?$

Use the Empirical Rule.
Use the sample statistics from Exercise 30 and assume the number of households in the sample is $40 .$
(a) Estimate the number of households whose monthly utility bills are between $\$ 54$ and $\$ 86$
(b) In a sample of 20 additional households, about how many households would you expect to have monthly utility bills between $\$ 54$ and $\$ 86 ?$

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Key Concepts

Empirical Rule

The empirical rule is a statistical guideline stating that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. This concept is vital for estimating the proportion of data points within a certain range when the data is assumed to be normally distributed.

Normal Distribution

A normal distribution is a symmetric, bell-shaped distribution that is common in many natural phenomena. It underpins the use of the empirical rule by providing a predictable pattern of data spread around the mean, allowing statisticians to estimate proportions of data within certain intervals.

Sample Size and Proportional Estimation

When dealing with sample statistics, the sample size plays a crucial role in estimating the count or proportion of events in a target range. By determining the percentage of data points from a normal distribution that fall within a specified interval, one can estimate the number of observations in a given sample size that would likely meet that criterion.

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