The distribution of scores on the SAT is approximately normal with a mean of u=500 and a standard deviation of o=100. For the population of students who have taken the SAT: a. What proportion have SAT scores less than 400? b. What proportion have SAT scores greater than 650? c. What is the minimum SAT score needed to be in the highest 20% of the. population? d. If the state college only accepts students from the top 40% of the SAT distribution, what is the minimum SAT score needed to be accepted?
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.
The distribution of scores on the SAT is approximately normal with a mean of u=500 and a standard deviation of o=100. For the population of students who have taken the SAT:
a. What proportion have SAT scores less than 400?
b. What proportion have SAT scores greater than 650?
c. What is the minimum SAT score needed to be in the highest 20% of the. population?
d. If the state college only accepts students from the top 40% of the SAT distribution, what is the minimum SAT score needed to be accepted?
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