Question

1. on the normal curve above what percentage of data values lie within two standard deviations of the mean (from -2σ to +2σ)?
2. here are some fun questions. make an educated guess 😊:

a. 95% of us women fall between what two heights?
b. 95% of us men fall between what two heights?

Explanation:

Step1: Recall the empirical rule for normal distribution

The empirical rule (68 - 95 - 99.7 rule) states that for a normal distribution:

• Approximately 68% of the data lies within \(1\sigma\) (i.e., \(\mu\pm\sigma\)) of the mean.
• Approximately 95% of the data lies within \(2\sigma\) (i.e., \(\mu - 2\sigma\) to \(\mu+2\sigma\)) of the mean.
• Approximately 99.7% of the data lies within \(3\sigma\) (i.e., \(\mu - 3\sigma\) to \(\mu+3\sigma\)) of the mean.

Step2: Apply the rule to the problem

Since we are asked for the percentage of data values within two standard deviations (\(- 2\sigma\) to \(+2\sigma\)) of the mean, by the empirical rule, the percentage is 95%.

Answer:

95%