Use z scores to compare the given values. In a recent awards ceremony, the age of the winner for best actor was 27 and the age of the winner for best actress were 47. For all best actors, the mean age is 42.7 years and the standard deviation is 7.7 years. For all best actresses, the mean age is 32.9 years and the standard deviation is 11.2 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain. Since the z score for the actor is z= and the z score for the actress is z=,the▼actress actor had the more extreme age.
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.
The Z-score of a random variable X is defined as follows:
Z = (X – µ)/σ.
Here, µ and σ are the mean and standard deviation of X, respectively.
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