Question

using the information given,
what is the value that goes in the red box?
the bell - shaped distribution has a mean of 28
and a standard deviation of 6.5
using the empirical rule, we know that 99.7%
of the data will fall between:

using the empirical rule, what percent of data falls within 1 standard
deviation of the mean?

Explanation:

Step1: Recall the Empirical Rule formula

The Empirical Rule states that for a normal distribution, \(99.7\%\) of the data lies within \(3\) standard deviations of the mean. The formula for the upper bound is \(\mu + 3\sigma\) and the lower bound is \(\mu - 3\sigma\). We know \(\mu = 28\), \(\sigma=6.5\), and the upper bound \(x = 47.5\). Let's use the lower - bound formula.

Step2: Calculate the lower bound

We use the formula \(x=\mu - 3\sigma\). Substitute \(\mu = 28\) and \(\sigma = 6.5\) into the formula:

$$
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Answer:

\(8.5\)