Percentiles of Certain Probability Distributions

distribution

N(0,1)

2

χ

(4)

T(20)

F(4,10)

percentile

0.6

The

th

p

percentile of a probability distribution is the point

x

p

, such that the area under the density to the left of

x

p

is

p

. In this Demonstration, the value of the

th

p

percentile is marked by the vertical segment. Notice that

p

is both the blue area—the area under the density to the left of

x

p

—and the

y

value marked by the horizontal red line—the value of the cumulative distribution function (the purple curve) at

x

p

.