The time, in minutes, taken by students to complete a test has the distribution $$\(\mathrm{N}(125,36)\)$$. Find the probability that the mean time taken to complete the test by a random sample of 40 students is less than 123 minutes. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_61 Year：2021 Question No：2(a)
Answer:
\( \pm \frac{123-125}{\frac{6}{\sqrt{40}}}[=-2.108 \ldots] \)
\( \mathrm{P}\left(z<{ }^{\prime}-2.108^{\prime}\right)=1-\Phi\left(\right. ' \left.2.108^{\prime}\right) \)
\( =0.0175\quad or\quad 0.0176(3 \mathrm{sf}) \)
\( \mathrm{P}\left(z<{ }^{\prime}-2.108^{\prime}\right)=1-\Phi\left(\right. ' \left.2.108^{\prime}\right) \)
\( =0.0175\quad or\quad 0.0176(3 \mathrm{sf}) \)
Knowledge points:
6.4.3 recognise that a sample mean can be regarded as a random variable, and use the facts that
6.4.4 use the fact that has a normal distribution if X has a normal distribution
Solution:
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