Question

Consider the data from the Anthropology 105 class. The mean is 64.33 in and the standard deviation is2.64 in.2. Label the heights at , + , − , + 2 etc. at the bottom of the normal curve below. (round to the hundredthsplace)______ _____ _____ _____ _____ _____ _____3. The middle 68% of women represented have a stature between what two heights? (round to the hundredths place)4. The middle 95% of women represented have a stature between what two heights? (round to the hundredths place)5. Write a sentence that uses the 95% range.

Answer 1

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:

$\begin{gathered} \mu=64.33in \\ \\ \mu-\sigma=64.33-2.64=61.69in \\ \\ \mu+\sigma=64.33+2.64=66.97in \\ \\ \mu-2\sigma=64.33-2*2.64=59.05in \\ \\ \mu+2\sigma=64.33+2*2.64=69.61in \\ \\ \mu-3\sigma=64.33-3*2.64=56.41in \\ \\ \mu+3\sigma=64.33+3*2.64=72.25in \end{gathered}$

The labels are then:

3. Following the empirical rule, the middle 68% of any normal distribution is within one standard deviation of the mean.

$\mu\pm\sigma=68\%$

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.

$\mu\pm\sigma=95\%$

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.