y from P(y) Mean and SD

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 Math

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.