Standard Normal Excel Equations and Normal Excel Equations
This guide is focused on foundational concepts needed for Applied Statistics as well as Intro to Statistics and assumes a general knowledge of how to navigate and use equations in excel. See the Microsoft office tech tutorial links for excel tutorials.
Probability distributions allow us to find the probability of being a certain number of standard deviations above or below the mean. When distributions are approximately normal, we can use the empirical rule to find probabilities for different values of (x).
Probability is found by calculating the area under the curve of a probability distribution. Finding this area requires calculus. But we can use excel equations to find the probability instead.
This guide builds on the concepts introduced in the Normal Distributions guide
Standard Normal Excel Equations
In a standard normal distribution, the mean is always 0 and the standard deviation is always 1.
To find probability when z-score is given: =NORM.S.DIST(z, true)
Gives the probability that a z-score is at or below a given value
To find the probability that a z-score is at or above a given value: =1—NORM.S.DIST(z, true)
To find the z-score when probability is given: =NORM.S.INV(probability)
Give the probability in decimal form (example: 45% = 0.45)
To find the probability between two values:
P(x< Z < b) = P(Z< b) – P(Z< x)
=NORM.S.DIST(b, true) – NORM.S.DIST(x, true)
| Find | Given | Equation | Symbols | Notes |
|---|---|---|---|---|
| Probability below | Z-score | =norm.s.dist(z, true) | z = z-score | Gives probability that a z-score is at or below a given value |
| Probability above | Z-score | =1 - norm.s.dist(z, true) | z = z-score | Gives probability that a z-score is at or above a given value |
| Z-score below | Probability | =norm.s.inv(probability) | Write probability in decimal form | Gives z-score for a probability at or below a given value |
| Z-score above | Probability | =norm.s.inv(1 - probability) | Write probability in decimal form | Gives z-score for a probability at or above a given value |
| Probability between | Two z-scores | =norm.s.dist(b, true) - norm.s.dist(x, true) |
b = higher z-score x = lower z-score |
Gives probability that a z-score is between two values (between x and b) |
General Normal Excel Equations
In general normal distribution, the mean and standard deviation can be anything.
To find probability of datum value x: =NORM.DIST(x, mean, standard deviation, true)
Gives the probability that x is at or below a given datum value
To find probability that x is at or above a given datum value: =1—NORM.DIST(x, mean, standard deviation, true)
To find x when a probability is given: =NORM.INV(probability, mean, standard deviation)
| Find | Given | Equation | Symbols | Notes |
|---|---|---|---|---|
| Probability below | Datum value | =norm.dist(x, mean, standard deviation, true) | x = datum value | Gives probability that a datum value is at or below a given value |
| Probability above | Datum value | =1 - norm.dist(x, mean, standard deviation, true) | z = z-score | Gives probability that a datum value is at or above a given value |
| Datum value below | Probability | =norm.inv(probability, mean, standard deviation, true) | Write probability in decimal form | Gives datum value for a probability at or below a given value |
| Datum value above | Probability | =norm.inv(1 - probability, mean, standard deviation, true)) | Write probability in decimal form | Gives datum value for a probability at or above a given value |
| Probability between | Two datum value | =norm.dist(b, mean, standard deviation, true) - norm.dist(x, mean, standard deviation, true) |
b = higher datum value x = lower datum value |
Gives probability that a datum value is between two values (between x and b) |
Next Steps:
Now that you know how to use the probability distribution excel equations, you’re ready to learn how to perform and make conclusions with hypothesis testing and confidence intervals.
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