The given distribution represents the height of the women in the anthropology class. The mean height is μ= 64.33in and the standard deviation is σ= 2.64in.
2. Using the given mean and standard deviation, you can determine the value of each label:
[tex]\begin{gathered} \mu=64.33in \\ \\ \mu-\sigma=64.33-2.64=61.69in \\ \\ \mu+\sigma=64.33+2.64=66.97in \\ \\ \mu-2\sigma=64.33-2*2.64=59.05in \\ \\ \mu+2\sigma=64.33+2*2.64=69.61in \\ \\ \mu-3\sigma=64.33-3*2.64=56.41in \\ \\ \mu+3\sigma=64.33+3*2.64=72.25in \end{gathered}[/tex]
The labels are then:
3. Following the empirical rule, the middle 68% of any normal distribution is within one standard deviation of the mean.
[tex]\mu\pm\sigma=68\%[/tex]
Then, you would find the middle 68% of the heights of the women within:
→ μ - σ= 61.69in
→ μ + σ= 66.97in
4. Following the empirical rule, 95% of the distribution is found within 2 standard deviations of the mean.
[tex]\mu\pm\sigma=95\%[/tex]
Then, you would find the middle 95% of the women's height will be found within:
→ μ - 2σ= 59.05in
→ μ + 2σ= 69.61in
5. You can define the middle 95% of the distribution as follows:
95% of the women in the anthropology 105 class are expected to have a stature between 59.05 inches and 69.61 inches.
