Suppose the time to complete a race for a particular age group are normally distributed with a mean of 27.2 minutes and a standard deviation of 3.3 minutes. Find the times that corresponds to the following z- scores. Round your answer to 3 decimals. a. Runner 1: z = 0.39, time b. Runner 2: z = - 1.61, time = c. Is Runner 1 faster than average, slower than average, or exactly average? O Faster than Average Slower than Average O Exactly Average d. Is Runner 2 faster than average, slower than average, or exactly average? O Faster than Average Slower than Average O Exactly Average
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.
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