# Question: The empirical rule states that the 1 2 and 3

The empirical rule states that the 1, 2, and 3 standard deviation intervals about the mean will contain 68%, 95%, and 99.7%, respectively.

a. Use the computer or calculator commands on page 90 to randomly generate a sample of 100 data from a normal distribution with mean 50 and standard deviation 10. Construct a histogram using class boundaries that are multiples of the standard deviation 10; that is, use boundaries from 10 to 90 in intervals of 10 (see the commands on pp. 52–54). Calculate the mean and the standard deviation using the commands found on pages 64 and 78; then inspect the histogram to determine the percentage of the data that fell within each of the 1, 2, and 3 standard deviation intervals. How closely do the three percentages compare to the percentages claimed in the empirical rule?

b. Repeat part a. Did you get results similar to those in part a? Explain.

c. Consider repeating part a several more times. Are the results similar each time? If so, in what way?

d. What do you conclude about the truth of the empirical rule?

a. Use the computer or calculator commands on page 90 to randomly generate a sample of 100 data from a normal distribution with mean 50 and standard deviation 10. Construct a histogram using class boundaries that are multiples of the standard deviation 10; that is, use boundaries from 10 to 90 in intervals of 10 (see the commands on pp. 52–54). Calculate the mean and the standard deviation using the commands found on pages 64 and 78; then inspect the histogram to determine the percentage of the data that fell within each of the 1, 2, and 3 standard deviation intervals. How closely do the three percentages compare to the percentages claimed in the empirical rule?

b. Repeat part a. Did you get results similar to those in part a? Explain.

c. Consider repeating part a several more times. Are the results similar each time? If so, in what way?

d. What do you conclude about the truth of the empirical rule?

**View Solution:**## Answer to relevant Questions

a. Use the computer commands on page 90 to randomly generate a sample of 100 data from a uniform (nonnormal) distribution that has a low value of 1 and a high value of 10. Construct a histogram using class boundaries of 0 to ...Did you know that 17.1% is more than double 15.6%? “Ridiculous!” you say. a. Explain how the graph suggests such a relationship. b. How could this misrepresentation be corrected? c. Redraw this graph to correctly show ...The American Time Use Survey presented at the beginning of the chapter outlined the time use of an average weekday for full-time university and college students. Category Hours Sleeping........... 8.3 Leisure and ...Gasoline pumped from a supplier’s pipeline is supposed to have an octane rating of 87.5. On 13 consecutive days, a sample of octane ratings was taken and analyzed, with the following results: a. Find the sample mean. b. ...The national highway system is made up of interstate and non interstate highways. The Federal Highway Administration reported the number of miles of each type in each state. Listed is a random sample of 20. Define “ratio ...Post your question