Find ACT quintiles. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores is normal with a mean of 21.5 and standard deviation of 5.4. The quintiles of any distribution are the values with cumulative proportions 0.20, 0.40, 0.60 and 0.80. What are the quintiles of the distribution of ACT scores?
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.
Find ACT quintiles. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores is normal with a
Let X be the ACT scores reported on a scale from 1 to 36
Given that X follows normal distribution with mean = 21.5 and standard deviation = 5.4
Quintiles are the values divide the distribution in to 5 parts.
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