The Boston Marathon is the oldest and best-known U.S. marathon. It covers a route from Hopkinton, Massachusetts, to downtown Boston. The distance is approximately 26 miles. Winning times for the Boston Marathon are all over 2 hours. The following data are the minutes over 2 hours for the winning male runners.   1961-1980 23 23 18 19 16 17 15 22 13 10 18 15 16 13 9 20 14 10 9 12   1981-2000 9 8 9 10 14 7 11 8 9 8 11 8 9 7 9 9 10 7 9 9 (a) Make a stem-and-leaf display for the minutes over 2 hours of the winning times for the years 1961 and 1980. Use two lines per stem. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks. For more details, view How to Split a Stem.) Minutes Beyond 2 Hours (1961-1980) (b) Make a stem-and-leaf display for the minutes over 2 hours of the winning times for the years 1981 to 2000. Use two lines per stem. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) Minutes Beyond 2 Hours (1981-2000) (c) Compare the two distributions. How many times under 15 minutes are in each distribution? 1961-1980      times 1981-2000      times

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.