The probability density function of the net weight in pounds of a packaged chemical herbicide if $f(x) = 2.0$ and $49.75<x<50.25$ pounds.

Question

How much chemical is contained in $90\%$ of all packages?

I understand that the value $90\%$ is a probability and I have to solve an equation to get value of $x$ corresponding to an inequality. However I fail to understand what is that equation. Either it is -

$$P(49.75<X<x) = 0.9,$$ or $$P(x<X<50.25) = 0.9.$$

How do I tackle such problems?

Answer 1

Since you know the density function $f(x)=2;x\in(49.75,50.25)$.

The first statement means that $90\%$ of the packages are under the weight $x$. The second statement is $90\%$ packages are above the weight $x$. This means that second statement is your answer.