(Solved): For a random variable x, a new random variable y can be created by applying a linear transformatio ...

For a random variable $$x$$, a new random variable $$y$$ can be created by applying a linear transformation $$y=a+bx$$, where $$a$$ and $$b$$ are constants. If the random variable $$x$$ has mean $${?}_{\mathrm{x}}$$ and standard deviation $${?}_{\mathrm{x}}$$, then the mean, variance and standard deviation of $$\mathrm{y}$$ are given by the following formulas. $${?}_y=a+b{?}_x{?}_y^2=b^2{?}_x^2{?}_y=?b?{?}_x$$ The mean annual salary for employees at a company is $$\$35,000$$. At the end of the year, each employee receives a $$\$3000$$ bonus and a $$10\%$$ raise (based on salary). What is the new mean annual salary (including the bonus and raise) for the employees? The new mean annual salary is $$\$$$