1. ## continuous prob

I have a function f(x) where f(x)=3/8*(7-x)^2 when 5<=x<=7 and 0 otherwise.

I calculated the E(x)=5.5
V(x)=.15
and Std dev=.378

Now, I have a question asking this-
Find an exact interval within which 80% of the pH measurements must lie with half of the other 20% of the pH measurements lying below the lower limit and the other half lying above the upper limit.

I know this is chebychev's thm. but I have no idea how to apply it in this case

2. Originally Posted by sfspitfire23
I have a function f(x) where f(x)=3/8*(7-x)^2 when 5<=x<=7 and 0 otherwise.

I calculated the E(x)=5.5
V(x)=.15
and Std dev=.378

Now, I have a question asking this-
Find an exact interval within which 80% of the pH measurements must lie with half of the other 20% of the pH measurements lying below the lower limit and the other half lying above the upper limit.

I know this is chebychev's thm. but I have no idea how to apply it in this case
$\int_5^a f(x) \, dx = 0.1$. Solve for a.

$\int^7_b f(x) \, dx = 0.1$. Solve for b.