Taylor and Meredith began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Taylor took a test in English and earned a 73.6, and Meredith took a test in Science and earned a 67.8. Use the fact that all the students' test grades in the English class had a mean of 70.1 and a standard deviation of 9.9, and all the students' test grades in Science had a mean of 63.5 and a standard deviation of 7.9 to answer the following questions.
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.
A z-score is the standard score that determines how much the data point deviates from the population mean (or the number of standard deviations above or below the mean value).
The formula of z score is,
The z score for Taylor grade is,
If the z-score is positive, it can be said that the data point lies above the mean value. In this case, as the z score is 0.35, it can be said that the student's score lies 0.35 standard deviations above the population mean.
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