Question

question number 4. (10.00 points) suppose you have a distribution, x, with mean = 15 and standard deviation = 6. define a new random variable y = 6x - 5. find the mean and standard deviation of y. options: ey=85, σy = 31; ey=90, σy = 31; ey=90, σy = 216; ey=85, σy = 216; ey=85, σy = 36; none of the above

Explanation:

Step1: Recall mean - transformation formula

The formula for the mean of a linear transformation of a random variable $Y = aX + b$ is $E[Y]=aE[X]+b$. Here $a = 6$ and $b=- 5$, and $E[X]=15$.
$E[Y]=6\times15-5$

Step2: Calculate the mean of Y

$E[Y]=90 - 5=85$

Step3: Recall standard - deviation transformation formula

The formula for the standard deviation of a linear transformation of a random variable $Y=aX + b$ is $\sigma_Y=\vert a\vert\sigma_X$. Here $a = 6$ and $\sigma_X = 6$.
$\sigma_Y=6\times6$

Step4: Calculate the standard deviation of Y

$\sigma_Y = 36$

Answer:

None of the above