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 $\int_{45}^{70}f(x)dx=0.5>0.35388$ and that $f(x)\geq 0$ for $20\leq x\leq 45$ so that $\int_d^{70}f(x)dx>0.35388$ for $d\leq 45$. Thus You can assume that $d>45$ and solve $$F(70)-F(d)=0,35388$$ where $F(x)=\frac{1}{625}(70x-\frac{1}{2}x²)$, 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 $A=\frac{ab}{2}$ where $A$ is the area of a right angled triangle with catheti $a$ and $b$. Then for example You can compute $\int_{45}^{70}f(x)dx=\underbrace{f(45)}_{=a}\underbrace{(70-45)}_{=b}\frac{1}{2}=\frac{1}{2}$ and similary $\int_{d}^{70}f(x)dx=f(d)(70-d)\frac{1}{2}=0.35388$ which of course leads You to the same quadratic equation that You should solve by completing the square as an exercise.