In a certain town, the time, $$$X$$$ hours, for which people watch television in a week has a normal distribution with mean $$$15.8$$$ hours and standard deviation $$$4.2$$$ hours. Find the probability that a randomly chosen person from this town watches television for less than 21 hours in a week. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_53 Year：2020 Question No：3(a)

Answer:

$\mathrm{P}(\mathrm{X}<21)=\mathrm{P}\left(z<\frac{21-15.8}{4.2}\right)=\Phi(1.238)$
$0.892$

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

Answer:

Knowledge points:

Solution:

Related Question