Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 62 minutes and a standard deviation of 8 minutes. Let X be a randomly selected finishing time.
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.
- What percent of the finish times was more than 72 minutes? (Give your answer to four decimal places)
- What percent of the finish times was between 52 and 70 minutes? (Give your answer to four decimal places)
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What is the 40th percentile finish time, ? 40? (Round your answer to nearest tenth)
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