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 probability that the weight of a randomly chosen apple of this variety differs from the mean weight by less than 4 grams. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

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

Answer:

$\Phi=0.7317$
Prob $=2 \Phi-1=2(0.7317)-1$
$=0.463$

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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