NORM.S.INV

Calculates the inverse of the standard normal cumulative distribution.

Syntax:

NORM.S.INV(probability)

probability is required, and is the probability associated with the standard normal distribution (a value between 0 and 1).

Example:

If probability contains 0.95:

NORM.S.INV(0.95)

returns 1.644853627

probability:

Result:

1.644853627

Application:

Let's imagine a company that manufactures widgets and wants to ensure that the widgets meet specific weight requirements. The company knows that the weight of the widgets follows a normal distribution with a mean of 50 grams and a standard deviation of 2 grams.

The company wants to set a tolerance for the widget weight, such that only 1% of the widgets will be rejected for being too light.

They can use the NORM.S.INV function to find the minimum weight a widget can be and still be in the acceptable range.

Here is a step-by-step example using a table:

Step 1: Find the z-score for the lower 1% tail of the standard normal distribution. We want to find the z-score that corresponds to a cumulative probability of 0.01.

	Probability	NORM.S.INV(Probability)	Description
	A	B	C
1	0.01	-2.326	This is the z-score below which 1% of the data falls.

The NORM.S.INV(0.01) function returns -2.326. This means that a z-score of -2.326 is the cutoff point for the lowest 1% of the data in a standard normal distribution.

Step 2: Convert the z-score to the actual weight using the formula: Weight = Mean + (z-score * Standard Deviation)

	Variable	Value
	A	B
1	Mean	50 grams
2	Standard Deviation	2 grams
3	z-score	-2.326

Step 3: Calculate the minimum weight: Weight = 50 + (-2.326 * 2) = 50 - 4.652 = 45.348 grams

Conclusion: The company should set the minimum acceptable weight for a widget at 45.348 grams. Any widget weighing less than this amount will be rejected, ensuring that only 1% of the total production is discarded for being too light.

Minimum weight:

45.348 grams