Use the normal distribution of IQ scores, which has a mean of 85 and a standard deviation of 11, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity Click the icon to view the table. - X O Data Table Percentage of scores less than 112.5 is %. (Round to two decimal places as needed.) Standard Scores and Percentiles for a Normal Distribution (cumulative values from the left) Full data set O Standard score % Standard % Score - 3.0 0.13 0.1 53.98 -2.5 0.62 0.5 69.15 -2 2.28 0.9 81.59 -1.5 6.68 1 84.13 - 1 15.87 1.5 93.32 -0.9 18.41 2 97.72 - 0.5 30.85 2.5 99.38 - 0.1 46.02 3 99.87 50.00 3.5 99.98
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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