In this assignment, you must use variables, loops, if statements, your own function definitions and function calls and callback functions. For now, you may NOT use any of the powerful functions available in python modules, with two exceptions: you may import functions from the math module and the copy module.

You must include docstrings for all your functions and reasonable comments throughout your code.

See your MAE $3013$ textbook for a reminder of:

The Secant Method for finding the solution $($root or zero$)$ or a nonlinear equation.

The Simpson's $\frac{1}{3}$ rule for numerical integration.

The Gauss$-$Sidel method in section $20\mathrm{.}3$

a$)$ Write a function defined as: lef Probability$($PDF$,$ args, $C,GT=$True $)$:

PDE: is a callback function for the Gaussian$/$normal probability density function $f(x)=\frac{1}{\sqrt[\phantom{2}]{2}}{e}^{-\frac{1}{2}(\frac{-}{}{)}^2}.$ The callback function $($PDF$)$ should take a single argument as a tuple, which contains values for $x,($population mean$),$ and $($population standard deviation$).$

args: is a tuple containing $$ and $$

c: is a floating point value $($i$.$e$,$ the upper limit of integration$)$

GT: is a boolean indicating if we want the probability of $x$ being greater than True$)$ or less than $C($GI$=$False$)$

To find the probability of

$P(x>181\mathrm{.}00|N(175,3))=Z.ZZx$ you should use the Simpson's$\frac{1}{3}$ rule $to$ integrate between the $limitsofx=-5*toC.$

Write and call a function that uses your function $to$ find:

: probability $x<mn\; id="EditorElement\_575485">1</mn><mn\; id="EditorElement\_575486">0</mn><mn\; id="EditorElement\_575487">5</mn>$ given a normal distribution $ofx$ with $=100,0=12\mathrm{.}5$

$P(x>+2|N(100,3))$

Print your findings $to$ the

$c.li.in$ the following format:

$P(x>181\mathrm{.}00|N(175,3))=Z.ZZ$