The first Stats exam had a mean of 70 and a standard deviation of 10 points; the second had a mean of 85 and a standard deviation of 5 points. Derrick scored an 85 on both tests. Julie scored a 75 on the first test and a 95 on the second. They both totaled 170 points on the two exams, but Julie claims that her total is better. Explain.
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 first Stats exam had a
and a standard deviation of
points; the second had a mean of
and a standard deviation of
points. Derrick scored
on both tests. Julie scored a
on the first test and
on the second. They both totaled
points on the two exams, but Julie claims that her total is better. Explain.
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