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Normsinv

For one reason or another, a number of people have for long underestimated the power of using excel for statistical calculations. This can be easily forgiven anyone because when most people were introduced to statistics at school (which they presumably forgot within minutes of graduation); they were not taught how to do it effectively using Microsoft Excel. However, as time goes on and people start to discover the need to use well designed tools, to make calculations and statistics as a whole much easier, they begin to look towards Excel.

Based on these reasons, it would be worth your time to briefly explore how to use Excel to create “bell-shaped” curves (otherwise known as normal curves) in Excel. In statistics, these curves occur quite frequently but can be difficult to implement in some cases; especially with larger data. In such instances, the power of Excel and its effectiveness come to play because it provides several useful functions (such as NORMSINV, NORMSDIST (z), NORMINV (probability, mean, standard_dev), STANDARDIZE (x, mean, standard_dev), NORMDIST (x, mean, standard_dev, cumulative) and more) that can handle this.

Normal Distribution Functions Explained:

NORMSINV (probability) - NORMSINV is a Microsoft Excel function that can be used to produce the inverse of the cumulative standardized normal distribution. In other words, NORMSINV is a probability function which returns a value x such that the integral from minus infinity to x of the standard normal distribution function is equal to P and P must be greater than 0 but less than 1.

The mathematical formulation is given by:

$\begin{displaymath} \mbox{{\it X}, such that} \; P = \int_{-\infty}^{X} \frac{1}{\sqrt{2\pi}} e^{-\frac{t^2}{2}} dt \end{displaymath}$

To implement the NORMSINV using Excel, you basically enter the "probability that a value x is up to..." and it returns that value x (in terms of "sigmas", because it is the standardized distribution with average 0 and sigma 1). For example: NORMSINV (0.5)=0, NORMSINV (0.00135)=-3, NORMSINV (0.9772)=2. NORMSINV (0) and NORMSINV (1) will return error, because they correspond to - infinite sigmas and +infinite sigma’s.

NORMSDIST (x) - On the other hand, the NORMSDIST function translates the number of standard deviations (x) into cumulative probabilities. This can be illustrated as below:

NORMSDIST (-1) = 15.87%
NORMSDIST (+1) = 84.13%

This means, the probability of a value being within one standard deviation of the mean is the difference between these values, or 68.27%. This range is represented by the shaded area of the chart.

In addition to all the information above, it might pay to not that NORMSINV is the inverse of NORMSDIST function. Furthermore, a number of cases where these normal curves occur are as listed below but may sometimes vary. They are:

Many Six-Sigma calculations assume normal distribution.
The number of staff turnover over a certain period is normally distributed
The number of defects in products as service has a normal distribution
Most measurement errors are assumed to be normally distributed.
The number of products and services sold over certain period in time assumes normal distribution
The measure of material used in a manufacturing process is usually normally distributed over time.
The width and weight of manufactured products are usually said to be normally distributed.
The number of customers, products delivered, and services rendered often assume a normal distribution depending on season or time of the year.

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