Question

11.1 using normal distributions (continued)
2 exploration: analyzing a data set
work with a partner. a famous data set was collected in scotland in the mid-1800s contains the chest sizes (in inches) of 5738 men in the scottish militia. do the data fit a normal distribution? explain.
table with chest size and number of men data
histogram of scottish militiamens chest sizes
communicate your answer

1. in a normal distribution, about what percent of the data lies within one, two, and three standard deviations of the mean?
2. use the internet or some other reference to find another data set that is normally distributed. display your data in a histogram.

Explanation:

This is based on the empirical rule (also known as the 68 - 95 - 99.7 rule) in statistics, which applies to normal distributions. The rule states these approximate percentages for data within 1, 2, and 3 standard deviations from the mean respectively.

Answer:

For a normal distribution:

• Approximately 68% of the data lies within one standard deviation of the mean.
• Approximately 95% of the data lies within two standard deviations of the mean.
• Approximately 99.7% of the data lies within three standard deviations of the mean.