4) Most medical schools in the U.S. require students to take the MCAT entrance exam. To estimate the mean score u of those who took the MCAT on your campus, you will obtain scores of an SRS of students. The scores follow a Normal distribution, and based on published information, the standard deviation is 6.5. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 25.0. a) If you choose one student at random, what is the probability that the student's score is between 20 and 30? b) You sample 25 students. What is the sampling distribution of their average score x-bar ? c) What is the probability that the mean score of your own sample is between 20 and 30?
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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