Question

Let X be the thickness of washers a machine turns out. Assume that x has the density f(x)=2.5x if 1.9 < x < 2.1 and 0 otherwish then calculate the probability that washer will have thickness between 1.95mm and 2.05 mm.

Answer 1

$$P(1.9\leq X\leq 2.1)=\displaystyle\int_{1.95}^{2.05}2.5xdx$$

$$=[1.25x^2]\begin{matrix} 2.05 \\ 1.95 \end{matrix}=1.25(2.05^2-1.95^2)$$

$$=0.5$$