Raj wants to improve his fitness, so every day he goes for a run. The times, in minutes, of his runs have a normal distribution with mean $$$41.2$$$ and standard deviation 3.6. Find the probability that on a randomly chosen day Raj runs for more than $$$43.2$$$ minutes. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_53 Year：2021 Question No：4(a)

Answer:

$P(X> 43.2)=P\left(Z> \frac{43.2-41.2}{3.6}\right)=P(Z> 0.5556)$
$1-\Phi(0.5556)=1-0.7108$
$0.289$

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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