Almost all medical schools in the United States require applicants to take the Medical College Admission Test (MCAT). On one exam, the scores of all applicants on the biological sciences part of the MCAT were approximately Normal with mean 9.8 and standard deviation 2.2. For applicants who actually entered medical school, the mean score was 10.4 and the standard deviation was 1.8. (a) What percent of all applicants had scores higher than 12? (b) What percent of those who entered medical school had scores between 9 and 11?
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.
Almost all medical schools in the United States require applicants to take the Medical College Admission Test (MCAT). On one exam, the scores of all applicants on the biological sciences part of the MCAT were approximately Normal with mean 9.8 and standard deviation 2.2. For applicants who actually entered medical school, the mean score was 10.4 and the standard deviation was 1.8.
(a) What percent of all applicants had scores higher than 12?
(b) What percent of those who entered medical school had scores between 9 and 11?
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