Question

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find Upper P 81​, which separates the bottom​ 81% from the top​ 19%. Round to two decimal places.

Answer 1

Answer:

(Upper P81) = 72.68

Step-by-step explanation:

Use the z-score formula:  

        x - mean

z = ------------------          Our goal:  find the x-value for the given inputs

           s. d.

Here we know s. d. (11.7) and mean (63.2)

Upper P81 is the upper boundary line of the area to the left of the left half  area 0.81:

          (Upper P81) - 63.2

0.81 = ----------------------------

                    11.7

Our job is to solve for (Upper P81).  Do this by multiplying both sides of this equation by 11.7, obtaining:

9.477 = (Upper P81) - 63.2, or

63.2 + 9.477 = (Upper P81), or, finally,

(Upper P81) = 72.68