Vtyjkyuk

I am trying to find the value of 'd' using the CASIO Classpad. I have been given a hybrid (piecewise) function and, having defined it on the calculator, I need to know the value of 'd' which will give Pr(T>=d)=0.35388..

However, this just doesn't seem to want to work.

Does anyone know where I am going wrong?

Here is a screenshot of the calculation. The limits of each function are between 20<=x<45 and 45<=x<=70 respectively.

Thanks in advance

PS. I'm fairly new to using the Classpad so apologies if this seems a basic question to ask.

Observe that $int_45^70f(x)dx=0.5>0.35388$ and that $f(x)geq 0$ for $20leq xleq 45$ so that $int_d^70f(x)dx>0.35388$ for $dleq 45$. Thus You can assume that $d>45$ and solve
$$F(70)-F(d)=0,35388$$
where $F(x)=frac1625(70x-frac12x²)$, which leads to a simple quadratic equation and even all this is overkill since the functions involved are linear and You just need to know the formula $A=fracab2$ where $A$ is the area of a right angled triangle with catheti $a$ and $b$. Then for example You can compute $int_45^70f(x)dx=underbracef(45)_=aunderbrace(70-45)_=bfrac12=frac12$ and similary $int_d^70f(x)dx=f(d)(70-d)frac12=0.35388$
which of course leads You to the same quadratic equation that You should solve by completing the square as an exercise.