Nick and Donald began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Nick took a test in Science and earned a 79.6, and Donald took a test in English and earned a 61.2. Use the fact that all the students' test grades in the Science class had a mean of 73.8 and a standard deviation of 9.3, and all the students' test grades in English had a mean of 66.2 and a standard deviation of 8.6 to answer the following questions. a) Calculate the z-score for Nick's test grade. z=z=__?__ b) Calculate the z-score for Donald's test grade. z=z=__?__ c) Which person did relatively better? __Nick __Donald __They did equally well.
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.
Nick and Donald began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Nick took a test in Science and earned a 79.6, and Donald took a test in English and earned a 61.2. Use the fact that all the students' test grades in the Science class had a mean of 73.8 and a standard deviation of 9.3, and all the students' test grades in English had a mean of 66.2 and a standard deviation of 8.6 to answer the following questions.
a) Calculate the z-score for Nick's test grade.
z=z=__?__
b) Calculate the z-score for Donald's test grade.
z=z=__?__
c) Which person did relatively better?
- __Nick
- __Donald
- __They did equally well.
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