A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1115 and a standard deviation of 206. Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 4.2. It is assumed that the two tests measure the same aptitude, but use different scales. If a student gets an SAT score that is the 68-percentile, find the actual SAT score. What would be the equivalent ACT score for this student? If a student gets an SAT score of 1321, find the equivalent ACT 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.
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are
- If a student gets an SAT score that is the 68-percentile, find the actual SAT score.
- What would be the equivalent ACT score for this student?
- If a student gets an SAT score of 1321, find the equivalent ACT score.
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