Assume that x is a random variable in a probability distribution with mean µ and standard deviation ?. Find expressions for the mean and standard deviation if every value of x is modified by first being multiplied by 3, then increased by 5.
A) $\mu _ { \text {new } } = 3 \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma + 5$
B) $\mu _ { \text {new } } = 3 \mu + 5$; $\sigma _ { \text {new } } = 3 \sigma$
C) $\mu _ { \text {new } } = 5 \mu + 3 ; \sigma _ { \text {new } } = 5 \sigma$
D) $\mu _ { \text {new } } = \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma$

Question

Assume that x is a random variable in a probability distribution with mean µ and standard deviation ?. Find expressions for the mean and standard deviation if every value of x is modified by first being multiplied by 3, then increased by 5. 
A) $\mu _ { \text {new } } = 3 \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma + 5$
B) $\mu _ { \text {new } } = 3 \mu + 5$; $\sigma _ { \text {new } } = 3 \sigma$
C) $\mu _ { \text {new } } = 5 \mu + 3 ; \sigma _ { \text {new } } = 5 \sigma$
D) $\mu _ { \text {new } } = \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma$

Quizplus · Accepted Answer

When a random variable $x$ is transformed into $3x + 5$, the mean $\mu$ is scaled and shifted to $3\mu + 5$, but the standard deviation $\sigma$ is only scaled by the factor of 3, not shifted, because standard deviation is a measure of spread and does not depend on the addition of constants.

Assume That X Is a Random Variable in a Probability μnew =3μ+5;σnew =3σ+5\mu _ { \text {new } } = 3 \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma + 5μnew ​=3μ+5;σnew ​=3σ+5

Assume That X Is a Random Variable in a Probability $\mu _ { \text {new } } = 3 \mu + 5 ; \sigma _ { \text {new } } = 3 \sigma + 5$