Assume That $\mathrm { x }$ Is a Random Variable in a Probability Distribution with Mean

Assume that $\mathrm { x }$ is a random variable in a probability distribution with mean $\mu$ and standard deviation $\sigma$ . Find expressions for the mean and standard deviation if every value of $\mathrm { x }$ is modified by first being multiplied by 5 , then increased by 4 .

A) $\mu _ { \text {new } } = 5 \mu + 4 ; \sigma _ { \text {new } } = 5 \sigma + 4$
B) $\mu _ { \text {new } } = 4 \mu + 5 ; \sigma _ { \text {new } } = 4 \sigma$
C) $\mu _ { \text {new } } = \mu + 4 ; \sigma _ { \text {new } } = 5 \sigma$
D) $\mu _ { \text {new } } = 5 \mu + 4 ; \sigma _ { \text {new } } = 5 \sigma$