question number 4. (10.00 points) suppose you have a distribution, x, with mean = 15 and standard deviation…

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. o ey = 85; σy = 31 o ey = 85; σy = 216 o ey = 90; σy = 31 o ey = 90; σy = 216 o ey = 85; σy = 36 o none of the above
Answer
Explanation:
Step1: Recall mean - transformation formula
If (Y = aX + b), then (E[Y]=aE[X]+b). Here (a = 6), (b=- 5) and (E[X]=15). [E[Y]=6\times15-5] [E[Y]=90 - 5=85]
Step2: Recall standard - deviation transformation formula
If (Y=aX + b), then (\sigma_Y=\vert a\vert\sigma_X). Here (a = 6) and (\sigma_X = 6). [\sigma_Y=6\times6 = 36]
Answer:
None of the above