Home / IB DP Math MAA HL : IB Style Mock Exams – Set 7 Paper 2

IB DP Math MAA HL : IB Style Mock Exams – Set 7 Paper 2

Question

[Maximum mark: 5]
There are 8 numbers in a data set. The sum of the numbers is 48 .

(a) Find the mean.                     [2]

The variance of this data set is 2 . Each number in the set is multiplied by 3 .

(b) Find the value of:
(i) the new mean;
(ii) the new variance.       [3]

Answer/Explanation

(a) We have
$
\begin{aligned}
\text { mean } & =\frac{48}{8} \\
& =6
\end{aligned}
$

(b) (i) We have
$
\begin{aligned}
\text { new mean } & =3 \times(\text { old mean }) \\
& =3 \times 6 \\
& =18
\end{aligned}
$

(ii) We have
$
\begin{aligned}
\text { new variance } & =3^2 \times(\text { old variance }) \\
& =3^2 \times 2 \\
& =18
\end{aligned}
$

Question

[Maximum mark: 6]
A random variable $X$ is normally distributed with $\mu=120$ and $\sigma=15$.
Find the interquartile range of $X$.

Answer/Explanation

If we draw the normal curve for $X$, we have


Hence, using $X \sim \mathrm{N}\left(120,15^2\right)$, we get
$
\begin{aligned}
& q_1=\operatorname{invNorm}(0.25,120,15) \approx 109.9 \\
& q_3=\operatorname{invNorm}(0.75,120,15) \approx 130.1
\end{aligned}
$

Hence we obtain
$
\begin{aligned}
\mathrm{IQR} & =q_3-q_1 \\
& =130.1-109.9 \\
& =20.2
\end{aligned}
$

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