NORMSINV

Calculates the inverse of the NORMSDIST function.

Syntax:

NORMSINV(p)

NORMSINV returns the value x, such that NORMSDIST(x) is p.

It is equivalent to NORMINV(p, 0, 1).

Example:

NORMSINV(0.5)

returns 0. Half of the standard normal distribution is below 0.

NORMINV(0.5, 0, 1)

also returns 0.

Application:

Setting Production Quality Control Limits

Scenario: A company produces machine parts, and the diameter of these parts is normally distributed. The company wants to set up a quality control system to identify parts that are too large or too small. They have determined that any part falling outside the middle 99.7% of the distribution is considered defective and needs to be inspected.

Goal: The quality control manager needs to find the Z-scores that correspond to the cutoff points for the top 0.15% and bottom 0.15% of the production. This will help them set up automated sensors that flag any part with a diameter corresponding to these Z-scores.

Calculations:

Identify the probabilities:
- The company wants to find the cutoff for the bottom 0.15% of production. This corresponds to a cumulative probability of 0.0015.
- To find the cutoff for the top 0.15%, we need to calculate the cumulative probability for that point. Since the total probability is 1, and we want to exclude the bottom 99.7% and the top 0.15%, we calculate: 1−0.0015=0.9985.
Use the NORMSINV function: The NORMSINV function takes a cumulative probability as its argument and returns the corresponding Z-score.
- For the bottom 0.15%: NORMSINV(0.0015)
- For the top 0.15%: NORMSINV(0.9985)

Table of Results:

	Cumulative Probability (p)	Z-Score (NORMSINV(p))	Interpretation
	A	B	C
1	0.0015	-2.968	This is the Z-score for the lower quality control limit. Any part with a diameter at or below this Z-score is in the bottom 0.15% and considered defective.
2	0.9985	2.968	This is the Z-score for the upper quality control limit. Any part with a diameter at or above this Z-score is in the top 0.15% and considered defective.

Conclusion:

Based on the NORMSINV function, the quality control manager knows that any part with a diameter that results in a Z-score less than -2.968 or greater than 2.968 is a defect. They can now set up their automated inspection equipment to flag any part that falls outside these limits, ensuring that only high-quality parts are approved for sale.