The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.6 years, with a standard deviation of 3.5. The winner in one recent year was 30 years old. Determine whether the age is unusual. Options: a) No, this value is not unusual. A z-score outside the range from -2 to 2 is not unusual. b) No, this value is not unusual. A z-score between -2 and 2 is not unusual. c) Yes, this value is unusual. A z-score between -2 and 2 is unusual. d) Yes, this value is unusual. A z-score outside of the range from -2 and 2 is unusual.
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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