Question

using the empirical rule, what percent of data falls within 1 standard deviation of the mean?
this is a required question
true or false: in order to use the empirical rule, you must first find the median for the data.
true
false
true or false: a bell - shaped distribution is when the data is symmetrical.
true
false
using the empirical rule:
the mean value of land and buildings per acre from a sample of farms is $300, with a standard deviation of $50. estimate the percent of farms

Explanation:

Step1: Recall the Empirical Rule

The Empirical Rule states that for a normal distribution:

• Approximately \(68\%\) of the data lies within \(1\) standard deviation of the mean (\(\mu\pm\sigma\)),
• Approximately \(95\%\) of the data lies within \(2\) standard deviations of the mean (\(\mu\pm2\sigma\)),
• Approximately \(99.7\%\) of the data lies within \(3\) standard deviations of the mean (\(\mu\pm3\sigma\)).

Step2: Analyze the second question

The Empirical Rule is applicable for a normal - distributed data set. It uses the mean (\(\mu\)) and the standard deviation (\(\sigma\)) of the data set. The median is not required for applying the Empirical Rule.

Step3: Analyze the third question

A bell - shaped distribution (normal distribution) is symmetric about the mean. That is, the left - hand side of the distribution (with respect to the mean) is a mirror image of the right - hand side of the distribution.

Answer:

1. \(68\%\)
2. False
3. True