The weights of apples of a certain variety are normally distributed with mean 82 grams. $$$22 \%$$$ of these apples have a weight greater than 87 grams. Find the standard deviation of the weights of these apples. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m20_qp_52 Year：2020 Question No：3(a)

Answer:

$\mathrm{P}(X>87)=\mathrm{P}\left(Z>\frac{87-82}{\sigma}\right)=0.22$
$\mathrm{P}\left(Z<\frac{5}{\sigma}\right)=0.78$
$\left(\frac{5}{\sigma}=\right) 0.772$
$\sigma=6.48$

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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