The lengths of female snakes of a particular species are normally distributed with mean $$$54 \mathrm{~cm}$$$ and standard deviation $$$6.1 \mathrm{~cm}$$$. Find the probability that a randomly chosen female snake of this species has length between $$$50 \mathrm{~cm}$$$ and $$$60 \mathrm{~cm}$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_51 Year：2020 Question No：6(a)

Answer:

$\mathrm{P}\left(\frac{50-54}{6.1}<z<\frac{60-54}{6.1}\right)=\mathrm{P}(-0.6557<Z<0.9836)$
Both values correct
$
\begin{array}{l}
\Phi(0.9836)-\Phi(-0.6557)=\Phi(0.9836)+\Phi(0.6557)-1 \\
=0.8375+0.7441-1 \\
\text { (Correct area })
\end{array}
$
0.582

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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