Cambridge International AS & A Level Mathematics 9709/51 May/June 2023 - Probability & Statistics 1

Vocabulary and key concepts from the Cambridge International AS & A Level Mathematics 9709/51 May/June 2023 Probability & Statistics 1 exam paper.

Standard Accuracy Requirement

Non-exact numerical answers should be given correct to $3$ significant figures, or $1$ decimal place for angles in degrees, unless specified otherwise.

Standard Deviation of $x$ (Coded Data)

A measure of spread calculated using summarized values where $n = 50$, $\Sigma(x - q) = 700$, and $\Sigma(x - q)^2 = 14235$.

Combination (Committee Selection)

The number of ways to choose a subset of items from a larger set where order does not matter, such as choosing $6$ people from $6$ men and $8$ women.

Permutations of COCOONED

The total number of different arrangements of the $8$ letters in the word COCOONED, accounting for repeated letters ($3$ Os and $2$ Cs).

Normal Distribution

A continuous probability distribution defined by a mean ($\mu$) and standard deviation ($\sigma$), used in the transcript to model puzzle completion times with $\mu = 14.6$ and $\sigma = 5.2$.

Histogram

A graphical representation of the population of $150$ villages categorized by class intervals ranging from $100-800$ to $3300-4800$.

Median Class Interval

The class interval in a grouped frequency table (e.g., village populations) that contains the middle value ($75.5\text{th}$ position for $150$ villages).

Interquartile Range (IQR)

The difference between the upper quartile ($Q_3$) and the lower quartile ($Q_1$); for the village data, the task is to find its greatest possible value.

Discrete Random Variable $X$

A variable denoting the number of times a specific outcome occurs in finite trials, such as the number of $2s$ obtained when throwing four fair $4$-sided dice.

Probability Distribution Table

A table listing all possible values of a random variable $X$ and their associated probabilities $P(X = x)$, where for four dice, $P(X = 3) = \frac{3}{64}$.

Expected Value $E[X]$

The mean or long-term average value of a random variable, calculated as $\Sigma (x \times P(X = x))$.

Normal Approximation to the Binomial Distribution

A method used to estimate probabilities for a large number of independent trials (e.g., throwing dice on $96$ occasions) when certain conditions are met.

Geometric Distribution (Scenario)

Used to find the probability of the first success occurring on or before a specific trial, such as finding an elephant model gift before the $6\text{th}$ Monday.

Binomial Distribution (Scenario)

Used to model the number of successes in a fixed number of independent trials, such as getting more than two leopards in $12$ magazines where the probability for each model is equal ($p = 0.2$).

List of Formulae (MF19)

The standard reference document provided for the Cambridge International AS & A Level Mathematics examinations.