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 1086 and a standard deviation of 202. Scores on the ACT test are normally distributed with a mean of 23 and a standard deviation of 4.9. It is assumed that the two tests measure the same aptitude, but use different scales.Normal CalculatorInverse Normal CalculatorIf a student gets an SAT score that is the 20-percentile, find the actual SAT score.SAT score = Round answer to a whole number.What would be the equivalent ACT score for this student?ACT score = Round answer to 1 decimal place.If a student gets an SAT score of 1288, find the equivalent ACT score.ACT score = Round answer to 1 decimal place. Get help: Written Example

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A: Answer:-

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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.