1. The mean score and the standard score in the Statistics test are respectively equal to 80 and 2.5, whereas in the Mathematics test they are respectively equal to 70 and 2. If Beth got a score of 85 in statistics and a score of 75 in Mathematics, in which subject is her standing better assuming normality in both subjects? 2. In an English test, the mean is 60 and the standard deviation is 6. Assuming the scores are normally distributed, what percent of the score is a. Greater than 65? b. Less than 70? c. Between 50 and 65?
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.
Instruction: Solve the following Problems:
1. The mean score and the standard score in the Statistics test are respectively equal to 80 and 2.5, whereas in the Mathematics test they are respectively equal to 70 and 2. If Beth got a score of 85 in statistics and a score of 75 in Mathematics, in which subject is her standing better assuming normality in both subjects?
2. In an English test, the mean is 60 and the standard deviation is 6. Assuming the scores are
a. Greater than 65?
b. Less than 70?
c. Between 50 and 65?
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