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?

Question

Julio Summers

Business

21 December, 21:26

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?

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Answers (1)

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Miles · Answer 1

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.