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

question 89

Multiple Choice

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) \(\mu _ { \text {new } } = 5 \mu + 4 ; \sigma _ { \text {new } } = 5 \sigma\)

---

Definitions:

Marginal Cost

The upswing in total financial outlay required for the production of one more unit of a good or service.

Profit Maximizing Condition

The specific point at which a firm's marginal revenue equals its marginal cost, leading to the highest possible profit.

Vertically Integrated

A business structure in which a company controls multiple stages of production or distribution within the same industry.

Net Marginal Revenue

The additional revenue generated from selling one more unit of a product or service after accounting for the marginal cost of producing that unit.