Reports on a student's ACT or SAT usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one. In 2007, composite ACT scores were close to Normal with mean 21.2 and standard deviation 5.0. Jacob scored 16. What was his percentile? 2) It is possible to score higher than 1600 on the SAT, but scores 1600 and above are reported as 1600. In 2007 the distribution of SAT scores (combining mathematics and reading) was close to Normal with mean 1021 and standard deviation 211. What proportion of 2007 SAT scores were reported as 1600?
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.
1) Reports on a student's ACT or SAT usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one. In 2007, composite ACT scores were close to Normal with mean 21.2 and standard deviation 5.0. Jacob scored 16. What was his percentile?
2) It is possible to score higher than 1600 on the SAT, but scores 1600 and above are reported as 1600. In 2007 the distribution of SAT scores (combining mathematics and reading) was close to Normal with mean 1021 and standard deviation 211. What proportion of 2007 SAT scores were reported as 1600?
3) The heights of women ages 20 to 29 follow approximately the N(64, 2.7) distribution. Men the same age have heights distributed as N(69.3, 2.8). What percent of young women are taller than the mean height of young men?
4) The heights of women ages 20 to 29 follow approximately the N(64, 2.7) distribution. Men the same age have heights distributed as N(69.3, 2.8). What percent of young men are shorter than the mean height of young women?
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