A football is compliant with regulations if it meets, depending on its size, two conditions simultaneously (on its mass and on its circumference). In particular, a standard-sized football is compliant with regulations when its mass, expressed in grams, belongs to the interval [410;450] and its circumference, expressed in centimetres, belongs to the interval [68;70].

\begin{enumerate}
  \item Let $X$ denote the random variable which, for each standard-sized football chosen at random in the company, associates its mass in grams.\\
It is admitted that $X$ follows a normal distribution with mean 430 and standard deviation 10.\\
Determine an approximate value to $10 ^ { - 3 }$ of the probability\\
$P ( 410 \leqslant X \leqslant 450 )$.
  \item Let $Y$ denote the random variable which, for each standard-sized football chosen at random in the company, associates its circumference in centimetres.\\
It is admitted that $Y$ follows a normal distribution with mean 69 and standard deviation $\sigma$.\\
Determine the value of $\sigma$, to the nearest hundredth, knowing that $97 \%$ of standard-sized footballs have a circumference compliant with regulations.\\
You may use the following result: when $Z$ is a random variable that follows the standard normal distribution, then $P ( - \beta \leqslant Z \leqslant \beta ) = 0,97$ for $\beta \approx 2,17$.
\end{enumerate}