Here is some information on the performance of their groups: The finishing times of the Men, Ages 30 - 34 group has a mean of 4311 seconds with a standard deviation of 594 seconds. The finishing times of the Women, Ages 25 - 29 group has a mean of 5277 seconds with a standard deviation of 781 seconds. The distributions of finishing times for both groups are approximately Normal. Remember: a better performance corresponds to a faster finish. 1. Write the short-hand for these two normal distributions. The Men, Ages 30 - 34 group has a distribution of N( The Women, Ages 25 - 29 group has a distribution of N( ). 2. What is the Z score for Leo's finishing time? z = 3. What is the Z score for Mary's finishing time? z =
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.
Triathlon times. In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in the Men, Ages 30 - 34 group while Mary competed in the Women, Ages 25 - 29 group. Leo completed the race in 4645 seconds, while Mary completed the race in 5606 seconds. Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Round all calculated answers to four decimal places.
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