IB Math AA SL — Statistics & Probability (Exam‑style)

Sure, juanzera22—here’s a mixed, exam‑style set for IB Math AA SL Statistics & Probability. It includes multiple‑choice and free‑response items in a Paper 1/2 style. IB Math AA SL — Statistics & Probability (Exam‑style) The data set is $\{\,2,4,4,5,7\,\}$. What is the mean? $4.4$ $4.2$ $4.0$ $5.0$ For the ordered data $\{\,3,5,6,8,9,11,12,13\,\}$, what is the interquartile range? $6$ $5$ $5.5$ $8$ Events $A$ and $B$ satisfy $P(A)=0.6$, $P(B)=0.5$, and $P(A\cap B)=0.3$. Find $P(A\cup B)$. $0.8$ $0.9$ $0.3$ $0.2$ $P(A)=0.3$ and $P(A\cap B)=0.12$. What is $P(B\mid A)$? $0.4$ $0.12$ $0.3$ $0.7$ Let $X\sim \mathrm{Bin}(n=5,\,p=0.4)$. Find $P(X=2)$ (to $3$ s.f.). $0.346$ $0.077$ $0.258$ $0.410$ Adult heights are modeled by $X\sim \mathrm{N}(\mu=170,\sigma=6)$. What is the $z$‑score of a person of height $182$? $2$ $-2$ $0.2$ $-0.2$ A dataset has product‑moment correlation $r=-0.85$. Which statement is correct? There is a strong negative linear correlation. There is a strong positive linear correlation. There is a weak negative linear correlation. There is no linear correlation. A discrete random variable $X$ takes values $0,1,2$ with probabilities $0.2,0.5,0.3$ respectively. What is $\mathbb E[X]$? $1.1$ $1.0$ $1.2$ $0.9$ Test scores are normally distributed with mean $\mu=68$ and standard deviation $\sigma=10$. (a) Find the proportion scoring above $80$. (b) Find the score corresponding to the $90^\text{th}$ percentile. (a) $z=\dfrac{80-68}{10}=1.2$, so $P(X>80)=1-\Phi(1.2)\approx 1-0.884=0.116\approx 0.115$. (b) For $p=0.90$, $z\approx 1.2816$, so $x=\mu+z\sigma=68+1.2816\times 10\approx 80.8$. A factory produces items with defect probability $p=0.03$ independently. Let $X\sim \mathrm{Bin}(n=20,\,p=0.03)$ be the number of defectives in a batch of $20$. (a) Find $P(X=1)$. (b) Find $P(X\le 1)$. (c) Find $\mathbb E[X]$. (a) $P(X=1)=\binom{20}{1}(0.03)(0.97)^{19}\approx 0.336$. (b) $P(X\le 1)=(0.97)^{20}+20(0.03)(0.97)^{19}\approx 0.880$. (c) $\mathbb E[X]=np=20\times 0.03=0.6$. A disease has prevalence $2\%$. A test has sensitivity $95\%$ and specificity $97\%$. (a) Draw a probability tree and compute $P(\text{positive})$. (b) Find $P(\text{disease}\mid \text{positive})$. (a) $P(+)=0.02\times 0.95+0.98\times 0.03=0.0484$. (b) $P(D\mid +)=\dfrac{0.02\times 0.95}{0.0484}\approx 0.393$. Least‑squares regression output (predicting $y$ from $x$): $\hat y=2.3+0.80x$, with $r=0.92$. Observed $x$‑values ranged from $0$ to $15$. (a) Interpret the slope. (b) Predict $y$ when $x=10$. (c) Comment on using the model to predict at $x=50$. (a) For each increase of $1$ unit in $x$, the model predicts an average increase of $0.80$ in $y$. (b) $\hat y=2.3+0.80(10)=10.3$. (c) $x=50$ is far outside the observed range, so extrapolation may be unreliable. The discrete random variable $X$ has $\Pr(X=0)=0.2$, $\Pr(X=1)=0.5$, $\Pr(X=2)=0.3$. (a) Find $\mathbb E[X]$. (b) Find $\mathrm{Var}(X)$. (a) $\mathbb E[X]=0(0.2)+1(0.5)+2(0.3)=1.1$. (b) $\mathbb E[X^2]=0^2(0.2)+1^2(0.5)+2^2(0.3)=1.7$, so $\mathrm{Var}(X)=\mathbb E[X^2]-\big(\mathbb E[X]\big)^2=1.7-(1.1)^2=0.49$. Two cards are drawn at random without replacement from a standard deck of $52$ cards. Find the probability that both cards are hearts. $\dfrac{13}{52}\times \dfrac{12}{51}=\dfrac{156}{2652}=\dfrac{1}{17}\approx 0.0588$. Want a matching markscheme for the multiple‑choice items, or a Paper $1$‑only (no‑technology) version next, juanzera22?

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