In a previous research project for University of Michigan, you wanted to know what extent students were a morning person. Using a scale from 1 (not a morning person) to 7 (very much a morning person), you had a mean of 3.40 and a standard deviation of 1.47. You examine your examine your data and find you have a student named Julian with a raw score of 6. 2.a. What is that student’s z score? 2.b. What percent of students are below Julian’s z score ? 2.c. What percent are above Julian’s z score?
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.
In a previous research project for University of Michigan, you wanted to know what extent students were a morning person. Using a scale from 1 (not a morning person) to 7 (very much a morning person), you had a mean of 3.40 and a standard deviation of 1.47. You examine your examine your data and find you have a student named Julian with a raw score of 6.
2.a. What is that student’s z score?
2.b. What percent of students are below Julian’s z score ?
2.c. What percent are above Julian’s z score?
You have another student, Monika from your university regarding they are a morning person or not. Her raw score is 1.0.
3.a. What is Monika’s z score?
3.b. What is the area (proportion ) between Monika and Julian’s Z scores ?
3.c. What is the area below Monika’s z score?
3.d What is the are above Monika’s z score?
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