C

The heights ($\mathrm{cm}$) of ten boys and their best performances ($\mathrm{cm}$) in standing long jump at the international athletic championship are listed in the following table. Determine the correlation coefficient $r$ between height of boys and their longest jump. You can use a statistics mode of your calculator to carry out statistical computations. Round the result to four decimal places. Based on the following scatterplot and the correlation coefficient interpret the strength of linear relationship between analysed variables. $$\begin{array}{|cccccc|}\hline \mathbf{\text{Boy's height (cm)}}& 189& 175& 187& 183& 174\\ \mathbf{\text{Length of the jump (cm)}}& 231& 207& 214& 223& 202\\ \\ \mathbf{\text{Boy's height (cm)}}& 193& 179& 169& 186& 183\\ \mathbf{\text{Length of the jump (cm)}}& 242& 229& 190& 226& 212\\ \hline\end{array}$$

The values of variables $x$ and $y$ are listed in the following table and visualized in the next graph. Calculate the correlation coefficient of $x$ and $y$ and round it to four decimal places. $$\begin{array}{|cccccc|}\hline x& 5& 6& 7& 9& 11\\ y& 3& 2& 4& 6& 8\\ \hline\end{array}$$

Students of a class take a multiple choice test consisting of $10$ tasks. There are $5$ optional answers to each of the tasks, while only one answer is correct. One student, however, did not study for the test at all. Therefore, he circles his answers randomly, without performing any calculations. Find the probability that he will circle at least $3$ correct answers. Round the result to four decimal places.

Suppose that the success rate of one specific medical treatment is $90\mathrm{\%}$. If the treatment is given to $20$ new patients, what is the probability that it is effective in at least $18$ of them? Round the result to four decimal places.