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`y = z( "P" ) * sigma + mu `

Enter a value for all fields

The **raw score from the Percentile, Mean and Standard Deviation** calculator computes the raw score (y) associated with a percentile rank (P) in a normal distribution with a mean (**μ**) and standard deviation (**σ**).

**INSTRUCTIONS:** Enter the following:

- (
**P**) This is the percentile ranking or probability of lesser values in a normal distribution. It has a range from 0.0 to 1.0 - (
**μ**) This is the mean of the normal distribution. - (
**σ**) This is the standard deviation of the normal distribution.

**Raw Score:** The calculator returns the raw score associated with the percentile ranking in the normal distribution. This raw score calculator is also a prominent feature with other statistical functions in the College Level Statistics Calculator (Stat Calc).

Example: A teacher says that the students with final exam grades in the top 5% of her class will go on a special field trip, and that the lowest 5% will have to write "I will study harder" a thousand times. If the final exam test scores are normally distributed with a mean of 72 and a standard deviation of 13.

- What is the cut off score for going on the field trip?
- P is 95% (0.95), mu is 72 and sd is 13. Using this calculator, what is the answer?

- What is the cut off score for having the writing assignment?
- P is 5% (0.05), mu is 72 and sd is 13. Using this calculator, what is the answer?

**RELATED CALCULATORS:**

- To compute the percentile of a single observation (y) in a set (X),
**CLICK HERE**. - To sort a list of numeric values,
**CLICK HERE.** - To create a random subset of the a list of numeric values,
**CLICK HERE**.

The formula for the z SCORE is as follows:

`z_y = (y - μ_X)/s` where:

- y is the single observation

- μ is the mean

- s is the sample or population standard deviation.

If we solve for y, the formula is as follows:

y = z * s + mu

Therefor we use the percentile ranking (P) to look up the z SCORE and compute the value of y.