The times taken to swim 100 metres by members of a large swimming club have a normal distribution with mean 62 seconds and standard deviation 5 seconds. $$\(13 \%\)$$ of the members of the club take more than $$\(t\)$$ minutes to swim 100 metres. Find the value of $$\(t\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_53 Year：2020 Question No：1(b)
Answer:
\(z=1.127\)
\(\frac{60 t-62}{5}=1.127\)
\(60 t=5.635+62=67.635\)
\(t=1.13\)
\(\frac{60 t-62}{5}=1.127\)
\(60 t=5.635+62=67.635\)
\(t=1.13\)
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. $Z=\frac{(X-\mu)}{\sigma}$)
Solution:
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