The time in hours that Davin plays on his games machine each day is normally distributed with mean $$\(3.5\)$$ and standard deviation $$\(0.9\)$$. Find the probability that on a randomly chosen day Davin plays on his games machine for more than $$\(4.2\)$$ hours. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_51 Year：2020 Question No：5(a)
Answer:
$
\begin{array}{l}
\mathrm{P}(\mathrm{X}>4.2)=\mathrm{P}\left(z>\frac{4.2-3.5}{0.9}\right)
=\mathrm{P}(z>0.7778)
\end{array}
$
\(1-0.7818\)
\(0.218\)
\begin{array}{l}
\mathrm{P}(\mathrm{X}>4.2)=\mathrm{P}\left(z>\frac{4.2-3.5}{0.9}\right)
=\mathrm{P}(z>0.7778)
\end{array}
$
\(1-0.7818\)
\(0.218\)
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 $x_{1}, \mu, \sigma$.
Solution:
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