# How to interpret a variable that represents a random error between -1 and 1?

In the storage of a stock of $100Kg$ flour bags, a random error $X$ is committed whose density function is of the form $f(x)=k(1-x^2)$, if $-1<x<1$ and $f(x)=0$, otherwise.

• $a)$ Calculate the probability that a sack of flour will pass from $99,5Kg$.
• $b)$ What percentage of sacks will have a weight between $99,8$ and $100,2Kg$?

My question is, the relationship between the error and the $100Kg$. Are we talking about a margin of error of $+1 Kg$ and $-1Kg$ respectively? That is:

In the part $a)$ I must calculate $P (X< -0.5)$ and in the part $b)$ $P (-0.2 <X <0.2)$?

Thank you very much.

• In this case it would be $1-P (X <-0.5)$? – emi Feb 13 '17 at 23:14
The only other possible interpretation I can think of is that $X$ is the percentage error, so that the final weight would be $100 (1+X)$. But, frankly, this would be quite a stretch.