## Excel Statistics Helper's Normal Distribution pre-made Excel Spreadsheet,  Just enter in data and get instant results! Excel Functions and Excel Formulas at the bottom of the page.

Searching for how to figure out how to find normal distribution in Excel from a z-score? How about the distribution between two z-scores or a x-value given z-score, standard deviation, and mean?

The Excel Normal Distribution Workbook has the normdist, normsdist, and normsinv functions pre-entered, just enter the variable(s) in the yellow cell, and get instant results!

Use again and again by entering in new variables in the yellow cells.

This Workbook has Spreadsheets that utilize:

• Excel Standard Normal Distribution function, (to the left and right) of a z-score

• Excel Standard Normal Distribution function (Standard Normal Curve Area Excel function) between two z-scores

• Normal Distribution Probabilities function in Excel (given mean, standard deviation, and x-value)

• Finding z-scores from a Standard Normal Cumulative Distribution function in Excel (Probability Percentile)

• Excel x-value function, given mean, standard deviation, and z-score (Excel transforming a z-score to an x-value function)

### Use this pre-made Excel Statistics Helper spreadsheet to calculate normal distribution in Excel!

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## Statistical definitions, Excel formulas, & Excel functions Performed in this Workbook:

Normal Distribution: A continuous probability distribution for a random variable (x).

A normal distribution, if graphed, it is called a Normal Curve. The normal distribution has the following attributes:

• The mean, median, and mode are all equal.
• The area under the curve is equal to 1.
• The normal curve is symmetrical about the mean, and is bell shaped.
• The normal curve nears, but never touches, the x-axis as it extends outward from the mean.

• Standard Normal Distribution- A normal distribution with a mean of "0" and a standard deviation of "1."

Microsoft uses different variations of the Excel functions NORMDIST, NORMSDIST, and NORMSINV to calculate different properties of a normal distribution. These Excel functions and Excel formulas will only apply if the data has a normal distribution.

Standard Normal Cumulative Distribution (probability)- In a standard normal distribution, z-scores can be used to find cumulative Standard Normal Distribution area. The Excel function NORMSDIST calculates this.

Since the standard normal distribution is a continuous probability distribution, the area under the standard normal curve to the left of a said z-score gives the probability that a random given z-score is less than the said z-score. For Example, the probability that a random given z-score, from a standard normal distribution, is less than z = 1.15 is 0.87 (~87%), and the probability that a random given z-score, from a standard normal distribution, is greater than z = 1.15 is 0.125 (~13%).

• Excel Standard Normal Cumulative Distribution function (given z-score): NORMSDIST
• Example Excel Standard Normal Cumulative Distribution formula (given z-score): =NORMSDIST(1.15)
• Example Excel Standard Normal Distribution formula area to the right of a given z-score: =(1-(NORMSDIST(1.15)))

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Standard Normal Distribution (Standard Normal Curve Area) between two z-scores- This will calculate the area under the standard normal curve between two z-scores. The Excel function NORMSDIST calculates this.

Since the standard normal distribution is a continuous probability distribution, the area under the standard normal curve to the left of a said z-score gives the probability that a random given z-score is less than the said z-score. To find the probability that a random given z-score will fall in between two said z-scores, calculate the difference between the area under the standard normal curve to the left of the larger said z-score and the area under the standard normal curve to the the left of the smaller said z-score. For example, the probability that a random given z-score, from a normal distribution, will fall in between z = 1.32 and z = -1.2 is .79 (79%).

• Excel Standard Normal Distribution Function (given z-score): NORMSDIST
• Example Excel Standard Normal Curve Area formula (left): =NORMSDIST(1.32)
• example Excel Standard Normal Curve Area formula (left): =(NORMSDIST(-1.2)
• Example Excel Standard Normal Curve Area formula between to z-scores: =(NORMSDIST(1.32)-(NORMSDIST(-1.2)))

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Normal Distributions and Probability (given x-value, mean, and standard deviation- If given a random variable (x-value) is in a normally distributed data set, probability of x falling into a given interval can be calculated if the mean and standard deviation are known. The Excel function NORMDIST calculates this.

Since a normal curve is equal to the standard normal distribution when the x-values are transformed into z-scores, they are the same within the corresponding z-boundaries. Therefore, if the mean and standard deviation are known, and an x-value is specified, the probability that a random given x-value will be less than the specified x-value can be calculated by finding the area under the standard normal curve to the left of the x-value. For example, if an x-value (215) is in a normal distribution, and the mean (236) and standard deviation (21) of the distribution is known, the probability that a randomly given x-value is less than 215 is .159 (~16%), and the probability that a random given x-value is greater than 215 is .841 (~84%).

• Excel Normal Distribution function: NORMDIST
• Example Excel Normal Distribution formula (left) =NORMDIST(215,236,21, TRUE)
• Example Excel Normal Distribution formula (right): =(1-(NORMDIST(215,236,21,TRUE)))

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z-scores from a Standard Normal Cumulative Distribution (Probability percentile)- The area under the Standard Normal Curve (probability percentile) can be converted to a z-score if the data is normally distributed. The Excel function NORMSINV calculates this.

Cumulative Area under the standard normal curve, or a percentile of a normally distributed data set, will have a corresponding z-score associated with it in the standard normal table. For example, a cumulative area (distribution) of 0.95, or the 95th percentile of normally distributed data, would correspond to a z-score of 1.64.

• Excel z-score from Normal Distribution: NORMSINV
• Example Excel z-score from Normal Distribution: =NORMSINV(0.95)

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Transforming a z-score to an x-value- To transform an x-value to a z-score, the following formula applies: z = ((x-µ)/σ).

Therefore, the following applies for transforming a z-score to an x-value:  x =  µ + z*σ. Below is how Excel Statistics Helper calculates this.

Below is how Excel Statistics Helper calculates this.

• Excel Transforming a z-score to an x-value: (mean+(standard deviation*z-score))
• Example Excel Transforming a z-score to an x-value formula: =(75+(6.5*1.64))

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For more information on the Excel Normal Distribution functions and Normal Distributions:

Statistical functions (reference) - Excel - Microsoft Office Online

Microsoft Excel Help and How-to Homepage

Normal Distribution - Wikipedia

Statistics Help @ Talk Stats Forum

Normal Distribution.xls

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