Wendy's journey to work consists of three parts: walking to the train station, riding on the train and then walking to the office. The times, in minutes, for the three parts of her journey are independent and have the distributions $$$\mathrm{N}\left(15.0,1.1^{2}\right), \mathrm{N}\left(32.0,3.5^{2}\right)$$$ and $$$\mathrm{N}\left(8.6,1.2^{2}\right)$$$ respectively. Find the probability that the mean of Wendy's journey times over 15 randomly chosen days will be less than $$$54.5$$$ minutes. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_62 Year：2021 Question No：4(c)

Answer:

$\frac{54.5-" 55.6 "}{\sqrt{\frac{14.9 "}{15}}}$ or $\frac{817.5-834}{\sqrt{223.5}}[=-1.104]$
$1-\phi\left(" 1.104^{\prime \prime}\right)$
$0.135(3 \mathrm{sf})$

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 $x_{1}, \mu, \sigma$.

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

Answer:

Knowledge points:

Solution:

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