Suppose $P_\text{tax}$ has a symmetric triangular distribution on $[1.2,1.9]$. Please answer:
a) The probability that $P_\text{tax}< 1.6$.
I have the following answer without the use of integrals:
triangle base $= 1.55-1.2$
triangle height $= 2/(1.9 - 1.2)$.
trapezoid height $= 1.6-1.55$
trapezoid 'bigger' base $= 2/(1.9-1.2)$
trapezoid 'smaller' base $= -4(1.6-1.9)/(1.2-1.9)^2$
Hence, the probability that $P_\text{tax}< 1.6$ is $0.5+0.2653 = 0.7653$.
Thank you for your help!