Question

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 mu Subscript xμx and standard deviation sigma Subscript xσx​, then the​ mean, variance and standard deviation of y are given by the following formulas. mu Subscript y Baseline equals a plus b mu Subscript xμy=a+bμx sigma squared Subscript y Baseline equals b squared sigma squared Subscript xσ2y=b2σ2x sigma Subscript y Baseline equals |b| sigma Subscript xσy=|b|σx The mean annual salary for employees at a company is ​$31 comma 00031,000. At the end of the​ year, each employee receives a ​$40004000 bonus and a 44​% raise​ (based on​ salary). What is the new mean annual salary​ (including the bonus and​ raise) for the​ employees?

Answer 1

Answer:

The new mean annual salary​ (including the bonus and​ raise) for the​ employees is $37790.

Explanation:

new salary Y = $4000 + 1.09X

new mean annual salary E(Y) = $4000 + 0.09*E(X)

                                                 = $4000 + 1.09*31000

                                                 = $37790

Therefore, The new mean annual salary​ (including the bonus and​ raise) for the​ employees is $37790.