New York City 10-km Run. As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 61 minutes and standard deviation 9 minutes. a. Determine the percentage of finishers who have times between 50 and 70 minutes.b. Determine the percentage of finishers who have times less than 75 minutes.c. Obtain and interpret the 40th percentile for the finishing times.d. Find and interpret the 8th decile for the finishing times.
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.
New York City 10-km Run. As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are
a. Determine the percentage of finishers who have times between 50 and 70 minutes.
b. Determine the percentage of finishers who have times less than 75 minutes.
c. Obtain and interpret the 40th percentile for the finishing times.
d. Find and interpret the 8th decile for the finishing times.
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