An elementary school class ran one mile with a mean of 12 minutes and a standard deviation of three minutes. Rachel, a student in the class, ran one mile in seven minutes. A junior high school class ran one mile with a mean of ten minutes and a standard deviation of two minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran one mile with a mean of eight minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in ten minutes. (a) Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he? (Round your standard deviations to two decimal places.) Kenji is considered a better runner than Nedda because Kenji's time for one mile was______ standard deviations_______ than the mean of his class and Nedda's time was______ standard deviations _______ than her class. b) Who is the fastest runner with respect to his or her class? Explain why. (Round your standard deviation to two decimal places.) _______was the fastest runner with respect to his/her class as he/she had a time that was_______ standard deviation(s) faster than his/her class.
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.
An elementary school class ran one mile with a mean of 12 minutes and a standard deviation of three minutes. Rachel, a student in the class, ran one mile in seven minutes. A junior high school class ran one mile with a mean of ten minutes and a standard deviation of two minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran one mile with a mean of eight minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in ten minutes.
(a) Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he? (Round your standard deviations to two decimal places.) Kenji is considered a better runner than Nedda because Kenji's time for one mile was______ standard deviations_______ than the mean of his class and Nedda's time was______ standard deviations _______ than her class.
b) Who is the fastest runner with respect to his or her class? Explain why. (Round your standard deviation to two decimal places.) _______was the fastest runner with respect to his/her class as he/she had a time that was_______ standard deviation(s) faster than his/her class.
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