Statistical studies have made it possible to model the weekly time, in hours, of internet connection for young people in France aged 16 to 24 years by a random variable $T$ following a normal distribution with mean $\mu = 13.9$ and standard deviation $\sigma$.
We know that $p ( T \geqslant 22 ) = 0.023$. By exploiting this information: a. shade on the graph provided in the appendix, two distinct regions whose area is equal to 0.023; b. determine $P ( 5.8 \leqslant T \leqslant 22 )$. Justify the result. Show that an approximate value of $\sigma$ to one decimal place is 4.1.
A young person in France is chosen at random. Determine the probability that they are connected to the internet for more than 18 hours per week. Round to the nearest hundredth.
Statistical studies have made it possible to model the weekly time, in hours, of internet connection for young people in France aged 16 to 24 years by a random variable $T$ following a normal distribution with mean $\mu = 13.9$ and standard deviation $\sigma$.
\begin{enumerate}
\item We know that $p ( T \geqslant 22 ) = 0.023$.
By exploiting this information:\\
a. shade on the graph provided in the appendix, two distinct regions whose area is equal to 0.023;\\
b. determine $P ( 5.8 \leqslant T \leqslant 22 )$. Justify the result. Show that an approximate value of $\sigma$ to one decimal place is 4.1.
\item A young person in France is chosen at random.
Determine the probability that they are connected to the internet for more than 18 hours per week.\\
Round to the nearest hundredth.
\end{enumerate}