(Solved): Example of answer: \( 24500 * \) For a random variable \( x \), a new random variable \( y \) can b ...

Example of answer: \( 24500 * \) For a random variable \( x \), a new random variable \( y \) can be created by applying a linear transtormation \( y= \) a \( + \) bx, where a and \( b \) are constants. If the random variable \( x \) has mean \( \mu_{x} \) and standard deviation \( \sigma_{x} \), then the mean, variance and standard deviation of \( y \) are given by the following formulas. \[ H_{y}=a+b \mu_{x} \quad d^{2} y=b^{2} \alpha^{2} x \quad \sigma_{y}=|b| \sigma_{x} \] The mean annual salary for employees at a company is \( \$ 36,000 \). At the end of the year, each employee receives a \( \$ 1000 \) bonus and a \( 5 \% \) raise (based on salary). What is the new mean annual salary (including the bonus and raise) for the employees? Your answer