Erik and Juan began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Erik took a test in Social Studies and earned a 72.8, and Juan took a test in Science and earned a 66.9. Use the fact that all the students' test grades in the Social Studies class had a mean of 72.2 and a standard deviation of 11.1, and all the students' test grades in Science had a mean of 64.2 and a standard deviation of 11 to answer the following questions. a) Calculate the z-score for Erik's test grade. z=z= [Round your answer to two decimal places.] b) Calculate the z-score for Juan's test grade. z=z= [Round your answer to two decimal places.]
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.
Erik and Juan began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Erik took a test in Social Studies and earned a 72.8, and Juan took a test in Science and earned a 66.9. Use the fact that all the students' test grades in the Social Studies class had a mean of 72.2 and a standard deviation of 11.1, and all the students' test grades in Science had a mean of 64.2 and a standard deviation of 11 to answer the following questions.
a) Calculate the z-score for Erik's test grade.
z=z= [Round your answer to two decimal places.]
b) Calculate the z-score for Juan's test grade.
z=z= [Round your answer to two decimal places.]
c) Which person did relatively better?
- Erik
- Juan
- They did equally well.
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