Two students, Emily and Jeremy, go to different schools and want to find out who has a higher GPA relative to the students at their own schools. Emily has a GPA of 3.60, and her school has a mean GPA of 3.10 and a standard deviation of 0.45. Jeremy has a GPA of 3.4, and his school has a mean of 3.05 and a standard deviation of 0.3. Who has the higher GPA when compared to each of their schools? Assume GPA has a normal distribution for each school. Justify your answer.
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.
Two students, Emily and Jeremy, go to different schools and want to find out who has a higher GPA relative to the students at their own schools.
- Emily has a GPA of 3.60, and her school has a mean GPA of 3.10 and a standard deviation of 0.45.
- Jeremy has a GPA of 3.4, and his school has a mean of 3.05 and a standard deviation of 0.3.
Who has the higher GPA when compared to each of their schools?
Assume GPA has a
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