Suppose we want to study the errors found in the performance of a simple task. We ask a large number of judges to report the number of people seen entering a major department store in one morning. Some judges will miss some people, and some will count others twice, so we do not expect everyone to agree. Suppose we find that the mean number of shoppers reported is 975 with a standard deviation of 15. Assume that the distribution of counts is normal. What percentage of the counts will lie between 960 and 990? What percentage of the counts will lie below 975?
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.
Suppose we want to study the errors found in the performance of a simple task. We ask a large number of judges to report the number of people seen entering a major department store in one morning. Some judges will miss some people, and some will count others twice, so we do not expect everyone to agree. Suppose we find that the mean number of shoppers reported is 975 with a standard deviation of 15. Assume that the distribution of counts is normal.
- What percentage of the counts will lie between 960 and 990?
- What percentage of the counts will lie below 975?
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