# Thread: Density curve

1. ## Density curve

=1/2xbasexheight

cannot work it out??? tried so many time

2. ## Re: Density curve

For the full triangle:
$\dfrac{1}{2}b\cdot h = 1$
$\dfrac{1}{2}(50-17)h = 1$
$h = \dfrac{2}{50-17}$

That is the height at 17. So, now you have a line from $(17,h)$ to $(50,0)$. Find the equation for that line and plug in 20 to determine the height at 20. Then, you want to find area again.

$y - y_1 = m(x-x_1)$

$y-0 = \dfrac{0-h}{50-17}(x-50)$

$y = \dfrac{-\dfrac{2}{50-17}}{50-17}(x-50) = -\dfrac{2}{(50-17)^2}(x-50)$

Plug in 20 to get the height at 20.

$y = \dfrac{60}{(50-17)^2}$

Now, calculate area:

$A = \dfrac{1}{2}b\cdot h = \dfrac{1}{2}(50-20)\cdot \dfrac{60}{(50-17)^2} = \dfrac{100}{121}$

That's your probability of $X\ge 20$.

To find $P(X<20)$, you need $1-\dfrac{100}{121} = \dfrac{21}{121}$