2. Invoice errors in a billing system. In a study of invoice errors in a company's new billing system, an auditor randomly sampled 90 invoices produced by the new system and recorded actual amount (A), invoice amount (I) and the difference (or “error"), x = (A – I). The results were a sample mean = $1 and standard deviation = $124 for the differences between the actual and invoice amounts. At the time that the sample was drawn, the new system had produced 1,500 invoices. Find an estimate for the true mean error per invoice of the new system. Interpret the results.
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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