The time in hours that Davin plays on his games machine each day is normally distributed with mean $$$3.5$$$ and standard deviation $$$0.9$$$. On $$$90 \%$$$ of days Davin plays on his games machine for more than $$$t$$$ hours. Find the value of $$$t$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_51 Year：2020 Question No：5(b)

Answer:

$z=-1.282$
$\frac{t-3.5}{0.9}=-1.282$
$t=2.35$

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. $Z=\frac{(X-\mu)}{\sigma}$)

Answer:

Knowledge points:

Solution:

Related Question