At a local high school, GPA's are normally distributed with a mean of 3.0 and standard deviation of 0.6. The middle 70% of the GPA values range from _____ to _____.
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.
- At a local high school, GPA's are
normally distributed with amean of 3.0 and standard deviation of 0.6. The middle 70% of the GPA values range from _____ to _____.
Let us denote X=GPA's at a local high school.
Given that X follows a normal distribution with mean= 3.0 and standard deviation = 0.6
If 70% is in the middle then 30% will be on both tails. So each tail will have 15%.
So upper tail has 15% =0.15 area.
The z score of that value is= 1.036
We use the z score formula to find the corresponding X value.
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