NORMINV

Calculates the inverse of the cumulative NORMDIST normal distribution function.

Syntax:

NORMINV(p, α, λ)

The normal distribution is a family of continuous probability distributions, with two controlling parameters α and λ.

NORMINV returns the value n, such that NORMDIST(n, α, λ, 1) is p.

Example:

NORMINV(0.92, 63, 5)

returns approximately 70.

Application:

The NORMINV function is useful when you have a known probability and want to find the corresponding value in a normal distribution. A common application is in quality control or financial analysis.

Let's consider a company that manufactures light bulbs. The lifespan of these light bulbs is normally distributed with a mean (μ) of 1,200 hours and a standard deviation (σ) of 150 hours. The company wants to determine the minimum lifespan for the top 10% of their most durable light bulbs.

Here's how you can use the NORMINV function to solve this problem:

The Goal: Find the lifespan value (x) such that the probability of a light bulb having a lifespan greater than x is 10%. This is the same as saying the probability of a light bulb having a lifespan less than or equal to x is 90% (or 0.9).

The Data:

	Parameter	Value	Description
	A	B	C
1	Probability	0.9	The cumulative probability we are interested in. Since we want the top 10%, this is equivalent to the bottom 90%.
2	Mean	1200	The average lifespan of the light bulbs.
3	Standard Deviation	150	The spread of the lifespan data.

The Formula:

The syntax for the NORMINV function is:

NORMINV(probability, mean, standard_dev)

The Calculation:

Using the values from our table, the function would be:

NORMINV(0.9, 1200, 150)

Result:

When you perform this calculation, the result is approximately 1392.23.

Conclusion:

This means that a light bulb with a lifespan of approximately 1,392.23 hours or more belongs to the top 10% of the most durable light bulbs manufactured by the company.

Result for NORMINV(0.9, 1200, 150):

1392.23