Trees in the Redian forest are classified as tall, medium or short, according to their height. The heights can be modelled by a normal distribution with mean $$$40 \mathrm{~m}$$$ and standard deviation $$$12 \mathrm{~m}$$$. Trees with a height of less than $$$25 \mathrm{~m}$$$ are classified as short. Find the height above which trees are classified as tall. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_52 Year：2020 Question No：4(c)

Answer:

$0.2981$ gives $z=0.53$
$\frac{h-40}{12}=0.53$
$h=46.4$

Knowledge points:

5.5.1 understand the use of a normal distribution to model a continuous random variable, and use normal distribution tables (Sketches of normal curves to illustrate distributions or probabilities may be required.)

5.5.2.2 finding a relationship between $x_{1}, \mu$ and $\sigma $ given the value of $P\left(X>x_{1}\right)$ or a related probability (For calculations involving standardisation, full details of the working should be shown.) (e.g. $Z=\frac{(X-\mu)}{\sigma}$)

Answer:

Knowledge points:

Solution:

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