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 probability that a randomly chosen tree is classified as short. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

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

Answer:

$\mathrm{P}(X<25)=\mathrm{P}\left(z<\frac{25-40}{12}\right)=\mathrm{P}(z<-1.25)$
$1-0.8944$
$0.106$

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.)

5.5.2.1 finding the value of $P\left(X>x_{1}\right)$, or a related probability, given the values of $x_{1}, \mu, \sigma$.

Answer:

Knowledge points:

Solution:

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