$x_1-x_2+3x_3+2x_4=,15$

$-x_1+5x_2-5x_3-2x_4=,-35$

$3x_1-5x_2+19x_3+3x_4=,94$

$2x_1-2x_2+3x_3+21x_4=,1$

$4x_1+2x_2+4x_3=,20$

$2x_1+2x_2+3x_3+2x_4=,36$

$4x_1+3x_2+6x_3+3x_4=,60$

$2x_2+3x_3+9x_4=,122$

b$)$ PLEASE DO NOT USE NUMPY, SCIPY.Also in homework $2,$ you used the Simpson numerical integration method to compute the area below the Gaussian$-$normal probability density function. In $$25\mathrm{.}3p1071,$ the t$-$distribution is used to calculate confidence intervals when the variance of the population is unknown. Write a program that computes the right hand side of the following equation and compare your results to Table $25\mathrm{.}2.$ You should test your program for $7,11,$ and $15$ degrees of freedom with three different $z$ values chosen by the user from the command line interface. Your program should prompt the user to input the degrees of freedom and value of $z$ and should output the probability.