Final exam scores in a mathematics course are normally distributed with a mean of 72 and a standard deviation of 5. Based on the above information and a Z-table, fill in the blanks in the table below. Precision and other notes: (1) Percentiles should be recorded in percentage form to three decimal places. (2) Note that this problem does not use the rough values of the 68-95-99.7 rule (that is, the empirical rule); instead you must use more precise Z-table values for percentiles. Exam score Z-score Percentile 87 67 0.67 2.28
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.
Final exam scores in a mathematics course are
Precision and other notes: (1) Percentiles should be recorded in percentage form to three decimal places.
(2) Note that this problem does not use the rough values of the
Exam score | Z-score | Percentile |
87 | ||
67 | ||
0.67 | ||
2.28 |
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