Business Math and Probability Practice Review

A set of vocabulary flashcards covering financial mathematics, calculus for business, and introductory probability and statistics based on practice problems.

Residential Natural Gas Bill Equation

The monthly charge calculation expressed as $y = 4.66 + 0.4803x$, where $4.66$ is the base service charge and $0.4803$ is the energy charge per hundred cubic feet $x$.

Profit Function $P(x)$

The expression representing total earnings after costs are deducted, calculated as $P(x) = R(x) - C(x)$. For example, if $R(x) = 500x$ and $C(x) = 100x + 4000$, then $P(x) = 400x - 4000$.

Break-even Point

The production level $x$ at which total revenue equals total cost, or the profit function $P(x) = 0$. In Problem 2, this occurs at $10$ computers.

Monthly Compounded Balance Function $S(t)$

The formula used to calculate a fund balance over $t$ months with a monthly interest rate, expressed as $S(t) = 300,000 \times (1 + \frac{0.1}{12})^{t}$ for a $10\%$ annual rate.

Ordinary Annuity

A series of equal payments made at the end of each period, such as a repeating payment of $\$1,000$ at the end of every $6$-month period.

Annuity Due

A series of equal payments made at the beginning of each period, such as monthly contributions to a college fund starting at a child's birth.

Average Cost $\bar{C}$

The cost per unit of production, defined by the formula $\bar{C} = \frac{C}{x}$, where $C$ is the total cost and $x$ is the production level.

Marginal Revenue $R'$

The rate of change of total revenue with respect to the number of units sold, represented as $R' = \frac{dR}{dx}$.

Marginal Profit $P'(x)$ Meaning

The derivative of the profit function representing the approximate change in profit from selling the $(x+1)^{\text{st}}$ unit. If $P'(200) = 50$, the sale of the $201^{\text{st}}$ unit increases profit by $\$50$.

Revenue Formula

The total income generated from sales, calculated as $R = \text{Quantity} \times \text{Price}$ or $R = x \times p$.

Yearly Rate of Flow $f(t)$

A continuous stream function, such as $f(t) = 10,000e^{0.05t}$, used to determine the total income over a period like the first $4$ years of operation.

Probability of At Least One Event

The likelihood that at least one of two events occurs, calculated using the formula $P(S \text{ or } E) = P(S) + P(E) - P(S \text{ and } E)$. Example: $0.80 + 0.70 - 0.65 = 0.85$.

Conditional Probability $P(A|B)$

The probability of event $A$ occurring given that event $B$ has already occurred, calculated as $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$.

Expected Value $\mu$

The mean or long-run average of a probability distribution, calculated as $\sum x \times P(x)$. In Problem 20, the expected number of cars is $\mu = 2$.

Variance $\sigma^2$

A statistical measure of the variability or spread of a probability distribution around the mean $\mu$. In Problem 20, the variance is $\sigma^2 = 1.4$.

Standard Normal Distribution

A normal distribution with a mean of $0$ and a standard deviation of $1$, where areas under the curve represent probabilities associated with z-scores.

Normal Distribution Mean and Standard Deviation

The central value ($\mu$) and the measure of variation ($\sigma$) of a bell-shaped data set. Example: A placement test with $\mu = 36 \text{ minutes}$ and $\sigma = 7 \text{ minutes}$.

Probability Without Replacement

The calculation of probability for successive events where the total pool decreases with each selection, such as picking $2$ faulty shirts from $100$ where only $5$ are faulty: $(\frac{5}{100}) \times (\frac{4}{99}) = \frac{1}{495}$.