There are lots of types of data that are approximately normal. For example, the heights of all the female students at Hope College would probably be a fairly normal distribution. For this lab, you are going to determine if the heights of a certain group of statistics students are close to normal as well as describe this distribution.

Get height data from the statistics web page. The heights given are in inches for 50 female statistics students (gender 1) and 50 male students (gender 2). Copy the data into a Minitab worksheet.

1. Calculate descriptive measurements for the heights of the males and the heights of the females.  (Stats > Basic Statistics > Display Descriptive Statistics.  For Variables: insert Height.  For By Variable: insert Gender.  Click OK.) Report each distribution's mean, median, and standard deviation. Only report the data asked for.

2. By comparing the means with the medians of each data set, what can you say about the symmetry of each data set?

3. Make stemplots of both data sets using split stem.  (Graphs > Stem-and-Leaf.  For Variables: insert Height.  For By Variable: insert Gender.  Set the Increment at 2.)

4. For each data set, determine the percentage of data that is within 1 standard deviation from the mean, the percentage of data that is within 2 standard deviations from the mean, and the percentage of data that is within 3 standard deviation from the mean. Using these results (and the 68-95-99.7 rule), comment on the normality of each data set.

5. Make a normal probability plot for each data set. (Graphs > Probability Plot. Click on Multiple and click OK.  For Variables: insert Height.  For By Variable: insert Gender.)  Using these results, comment on the normality of each data set.  If the data are fairly normal, the points will appear close to the line in a normal probability plot and almost all the points will be within the probability bands.

6. Suppose that the mean and standard deviation all females at Hope were those found in question 1.  What proportion of all female students at Hope have heights less than 65 inches?  More than 70 inches?  (Use Calc > Probability Distributions > Normal. Click on Cumulative Probability, input the mean and standard deviation found in question 1, click on input constant, and input either the 65 or the 70.  Be careful with direction of this cumulative probability.)