The ACT math scores of a particular high school in New Jersey are approximately normally distributed. Within this curve, 99.7% of the scores, centered about the mean, are between 200 points and 800 points. The standard deviation is 100 points. Use this information to estimate the mean of the math scores for the high school. Approximate the probability that a score is less than 400 points. Explain how you determined your answers
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.
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