An elementary school class ran one mile with a mean of 11 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 seven minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in eight 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 ---Select--- slower faster than the mean of his class and Nedda's time was standard deviations ---Select--- slower faster 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.) ---Select--- Kenji Nedda Rachel 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 11 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 seven minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in eight minutes.
(b) Who is the fastest runner with respect to his or her class? Explain why. (Round your standard deviation to two decimal places.)
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