Every question, cut by section

Which of these best describes what a mathematical model is, in the sense spec item 1.1 means it?

For a frequency table with midpoints $x$, frequencies $f$, and $n = \Sigma f$, which expression correctly defines the standard deviation?

Let $N$ = 'a customer buys a newspaper' and $M$ = 'a customer buys a magazine'. Which expression correctly represents 'the probability a customer buys a magazine, GIVEN that they have already bought a newspaper'?

A Venn diagram for a class of 60 students and events $A$ (studies French) and $B$ (studies Spanish) shows 18 students in $A$ only, 22 in $B$ only, and 12 in both. How many students are outside both circles, and how should that be shown on the diagram?

A regression line is fitted to data recorded for $x$ between 10 and 50. Which of these predictions is NOT extrapolation?

A discrete random variable $X$ has $\text{Var}(X) = 9$. Student 1 finds $\text{Var}(3X)$; Student 2 finds $\text{Var}(-3X)$. Which statement is correct?

A question begins: "A fair six-sided die is rolled once." What does the word "fair" actually license you to write down?

A data set $X$ is coded as $Y = (X - 40) / 4$. Given $\text{Var}(Y) = 5$, what is $\text{Var}(X)$?

A weather forecaster writes $P(\text{rain tomorrow} \mid \text{cloudy today}) = 0.6$. What does this number represent?

A bag contains 5 counters: 2 red and 3 green. Two counters are drawn at random, WITH replacement. What is $P(\text{both red})$?

A student correctly finds $S_{xx} = 25$ and $S_{xy} = 40$ for a dataset, and correctly finds $\bar x = 4$, $\bar y = 11$. Which of these is an acceptable way to state the final regression line?

A company pays each employee a monthly bonus, in dollars, $B = 50N - 20$, where $N$ is the random number of new clients that employee brings in that month. Records show $E(N) = 4$ and $\text{Var}(N) = 1.5$. Find $E(B)$ and $\text{Var}(B)$.

A question states "model the journey times as Normally distributed," then later shows a box plot of the same data with strong positive skew. What does this situation best illustrate?

A student's working for the standard deviation of a set of exam scores (out of 100) produces a final answer of 236. What should immediately raise suspicion, beyond re-checking the algebra?

A card is drawn from a standard 52-card deck (4 Kings, 4 Queens, 44 others). Given that the card is a King or a Queen, find the probability it is a King.

A spinner is divided into 5 equal sections: 3 blue and 2 yellow. It is spun twice. What is $P(\text{exactly one yellow})$?

Using the fitted line $\hat y = 10.1 + 4.25x$ from this lesson's dataset, a manager notices weekly enquiries have risen by 21.25 compared to a previous week. According to the model, how much extra was spent on advertising (in dollars) to produce that rise?

Which of the following would you need to recall from memory in a WST01 exam, rather than being able to look up in the Mathematical Formulae and Statistical Tables booklet?

In the real WST01 question this lesson's worked chain is built from (Jan 2025, Q1), a second die — blue, with faces numbered 1, 3, 5, 7 — is also stated to be fair, and its score is modelled by $B$. Which of these correctly describes $B$'s distribution, and why?

A frequency table has values 10, 20, 30, 40 with frequencies 3, 5, 7, 5 ($\Sigma f = 20$). What is the mean?

Three fair coins are tossed. By listing the sample space systematically, find $P(\text{exactly two heads})$.

A bag contains 8 counters: 5 green and 3 blue. Three counters are drawn at random, one after another, without replacement. What is $P(\text{all three the same colour})$?

A discrete random variable $X$ can take the values $0, 1, 2$ and $3$ only. A student writes $p(1) = 0.2$, $p(2) = 0.4$, $p(3) = 0.3$ and stops, treating this as the complete probability function. What does checking $\sum p(x) = 1$ reveal?

$X \sim N(30, 4^2)$. A student wants $P(X < 34)$. After standardising to $z = 1$ and reading $\Phi(1) = 0.8413$ from the table, what should they do next?

A question models daily rainfall as Normally distributed, then later states that real data shows a small number of days with far higher rainfall than the model predicts as at all likely, while ordinary days fit the model well. Which response best identifies what's happening, in the terms this lesson has used?

A grouped frequency table has $n = 39$. One student finds $Q_1$'s position using $n/4 = 9.75$; another uses $(n+1)/4 = 10$. Both interpolate correctly from their own position within whichever class it falls into. What's true of their two final answers?

Events $A$ and $B$ satisfy $P(A) = 0.3$, $P(B) = 0.4$, and $P(A \cap B) = 0$. What can you correctly conclude?

You already know how to find $S_{xx}$ and $S_{xy}$ for a regression line. To find $r$, the product moment correlation coefficient, you need one more summary quantity. Which one, and why does the gradient $b$ never need it?

A discrete random variable $Y$ has probability function $p(y) = cy$ for $y = 1, 2, 3, 4$, where $c$ is a constant. What is the FIRST line of working needed to find $c$?

A question requires the value of $z$ such that $P(Z > z) = 0.05$. The Percentage Points of the Normal Distribution table gives this value to 4 decimal places. Which written answer is correct exam technique?

Spec 1.1 is examined through AO3, worth 15-20 of this paper's 75 marks — and the reviewed past-paper record shows this content is embedded inside other questions rather than tested as a standalone question of its own. What does this mean practically for how to revise it?

Group C has 20 data values, mean 45, standard deviation 3. To combine it with another group, you need $\Sigma x^2$ for Group C. Which expression is correct?

Of 150 people surveyed, 60 own a car ($C$) and 45 own a bicycle ($B$); 20 own both. Find $P(C \mid B)$.

A large, unwieldy dataset is coded (e.g. subtracting a fixed value and dividing by another) purely to make the arithmetic manageable before finding its PMCC. Which best describes how that coding affects the actual value of $r$?

A discrete random variable $W$ is Discrete Uniform on the values $\{5, 10, 15, 20\}$ — these four values are equally likely. What is $p(10)$?

$M \sim N(\mu, \sigma^2)$. A question gives you that $M > 40$, and asks for $P(M > 55 \mid M > 40)$. What kind of calculation is this?

A histogram bar for the class $4 \leq x < 8$ (width 4) has height (frequency density) 5. What is the frequency for this class?

A data set has $Q_1 = 20$ and $Q_3 = 32$. Using the rule "a value is an outlier if it is more than $1.5 \times IQR$ beyond the nearer quartile," what is the correct LOWER fence?

Two fair six-sided dice are rolled. $A$ = 'the first die shows a 6'. $B$ = 'the two dice sum to 7'. Are $A$ and $B$ independent?

A calculation for $r$ involves dividing by a square root — for example, $90 \div \sqrt{15000}$ — and the final answer needs to be given to 3 significant figures. What's the safest amount of precision to use for the square root itself, before dividing?

A discrete random variable $X$ takes the values 1, 2, 3, 4 with $p(1)=0.1$, $p(2)=0.2$, $p(3)=0.3$, $p(4)=0.3$. A student checks that every one of these four numbers lies between 0 and 1, and concludes this is a valid probability function. Is the student's check sufficient?

$X \sim N(40, 6^2)$. Find $P(X < 46)$.

In a back-to-back stem-and-leaf diagram, which leaf represents the SMALLEST value on the LEFT-hand side of a row?

A data set contains one very large outlier. Why might the median be quoted as "a typical value" rather than the mean?

Events $C$ and $D$ satisfy $P(C) = 0.6$, $P(D) = 0.5$, and $P(C \cap D) = 0.3$. Are $C$ and $D$ independent, mutually exclusive, both, or neither?

For a dataset, $S_{xx} = 16$, $S_{yy} = 25$, $S_{xy} = 18$. What is the product moment correlation coefficient $r$?

A discrete random variable $X$ has $p(1)=0.15$, $p(2)=0.35$, $p(3)=0.25$, $p(4)=0.25$. Find $F(3)$.

A question needs the z-value satisfying $P(Z > z) = 0.05$. Which value should be written down?

When a question asks you to compare two distributions, which response earns full marks?

A box plot's upper fence, from the rule given in the question, works out at 50. The data's true maximum is 61, which the rule identifies as an outlier; the highest value that is NOT an outlier is 46. Where should the upper whisker actually end?

In a class, $P(\text{studies Chemistry}) = 0.5$, $P(\text{studies Biology}) = 0.6$, and $P(\text{studies both}) = 0.2$. Find $P(\text{Biology} \mid \text{NOT Chemistry})$.

A dataset is coded using $u = \dfrac{x-50}{5}$ and $v = \dfrac{y-20}{2}$ to simplify the arithmetic. The PMCC of the coded data, $r_{uv}$, is found to be $0.64$. What is $r$ for the original, uncoded $x$ and $y$ data?

A discrete random variable $T$ is Discrete Uniform on $\{3,6,9,12,15\}$. Using symmetry, what is $E(T)$?

$Y \sim N(70, 10^2)$. Given that $P(Y < y) = 0.05$, find the value of $y$.

A histogram bar for the class $8 \leq x < 12$ (width 4) has height (frequency density) 6.5. What is the frequency for this class?

A data set has $Q_1 = 18$ and $Q_3 = 30$. Using the rule "an outlier is a value more than $1.5 \times IQR$ beyond the nearer quartile," is the value 47 an outlier?

Events $E$ and $F$ satisfy $P(E) = 0.2$, $P(F) = 0.3$, $P(E \cap F) = 0.06$. A student writes: 'E and F are independent, because their probabilities are both small, so they can't really affect each other.' Is the student's final answer correct, and is the reasoning acceptable?

A question asks: 'Find r, giving your answer to 3 significant figures,' and your working reaches the step $90 \div \sqrt{15000}$. What's the safest way to evaluate this?

A discrete random variable $U$ is Discrete Uniform on $\{2,4,6\}$. Find $\text{Var}(U)$.

$M \sim N(25, 4^2)$. Given that $M > 20$, find $P(M > 28 \mid M > 20)$.

Class P: width 10, frequency density 2. Class Q: width 3, frequency density 5.

Which class contains MORE data values?

For this data (Q1 = 40, Q3 = 52), a value is defined as an outlier if it lies more than 2 × IQR beyond the nearer quartile.

Is the value 73 an outlier, under the rule as stated in THIS question?

Two fair six-sided dice are rolled. $A$ = 'the first die shows a 6' and $B$ = 'the two dice sum to 7' — the same pair of events already shown earlier in this lesson to be independent. Which of the following events $D$ is mutually exclusive with $A$, but still has $P(B \cap D) > 0$?