Question

this data is normally distributed. what percent of the data is in the shaded region?

Explanation:

Step1: Recall the empirical rule for normal distribution

The empirical rule states that for a normal distribution:

• Approximately \(68\%\) of the data lies within \(1\) standard deviation (\(\sigma\)) of the mean (\(\bar{x}\)), i.e., \(\bar{x}\pm1\sigma\)
• Approximately \(95\%\) of the data lies within \(2\) standard deviations (\(\sigma\)) of the mean (\(\bar{x}\)), i.e., \(\bar{x}\pm2\sigma\)
• Approximately \(99.7\%\) of the data lies within \(3\) standard deviations (\(\sigma\)) of the mean (\(\bar{x}\)), i.e., \(\bar{x}\pm3\sigma\)

Step2: Analyze the shaded region

The shaded region is from \(- 1\sigma\) to \(+1\sigma\) around the mean \(\bar{x}\)

Answer:

\(68\%\)