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

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Definitions:

Full Capacity

The maximum level of output that a company can produce under normal conditions over a given time period.

EFN

Expected Funds Needed, an estimation of the additional financing a company will require in the future based on its projected growth and existing financial structure.

Sustainable Growth Rate

The maximum rate at which a company can grow its sales and earnings without increasing leverage or debt financing.

Leverage Ratios

Financial metrics that assess the level of debt in a company's capital structure relative to its equity or assets.