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Solved: Linear Transformation of a Random Variable In
Chapter 4, Problem 40EC(choose chapter or problem)
In Exercises 39 and 40, use the following information. 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 \(\mu_x\) and standard deviation \(\sigma_x\), then the mean, variance, and standard deviation of y are given by the formulas below.
\(\mu_y=a+b\mu_x\) \(\sigma_y^2=b^2\sigma_x^2\) \(\sigma_y=|b|\sigma_x\)
The mean annual salary of employees at a company is $36,000 with a variance of 15,202,201. At the end of the year, each employee receives a $2000 bonus and a 4% raise (based on salary). What is the standard deviation of the new salaries?
Equation Transcription:
Text Transcription:
y=a+bx
mu_x
mu_y=a+b{mu}_x
sigma_y^2=b^2sigma_x^2
sigma_y=|b|sigma_x
Questions & Answers
QUESTION:
In Exercises 39 and 40, use the following information. 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 \(\mu_x\) and standard deviation \(\sigma_x\), then the mean, variance, and standard deviation of y are given by the formulas below.
\(\mu_y=a+b\mu_x\) \(\sigma_y^2=b^2\sigma_x^2\) \(\sigma_y=|b|\sigma_x\)
The mean annual salary of employees at a company is $36,000 with a variance of 15,202,201. At the end of the year, each employee receives a $2000 bonus and a 4% raise (based on salary). What is the standard deviation of the new salaries?
Equation Transcription:
Text Transcription:
y=a+bx
mu_x
mu_y=a+b{mu}_x
sigma_y^2=b^2sigma_x^2
sigma_y=|b|sigma_x
ANSWER:
Solution:
Step 1 of 1:
Our goal is:
We need to find the standard deviation of the new annual salary.