Find the probability that a randomly chosen student plays rugby given that he plays soccer.

Find \(k \) if the game is fair.

\( \begin{array} {|c|c|c|c|c|} \hline
x & 15 & 20 & 35 & -40 \\ \hline
P( X = x ) & 0.1 & k & 0.3 & 2k \\ \hline
\end{array} \)

Let \(X\) represent the discrete random variable ‘number of fives’ obtained in three dice. Find the largest number for \(X\).

Find \(P\left( {X > 2} \right)\).

\( \begin{array} {|c|c|c|c|c|c|} \hline
x & 0 & 1 & 2 & 3 & 4 \\ \hline
P( X = x ) & 0.2 & 0.3 & 0.2 & 0.1 & 0.2 \\ \hline
\end{array} \)

The table shows Amy’s results for two tests.   Which test is the better result for Amy compared to her class?

\( \begin{array}{|c|c|c|c|} \hline
\text{test} & \text{Amy’s result} & \text{class mean} & \text{class standard deviation} \\ \hline
A & 82 & 75 & 7 \\ \hline
B & 86 & 77 & 10 \\ \hline
\end{array} \)

Find the population standard deviation of the following data set, correcting to two decimal places using technology.

\(\begin{array} {|c|c|c|c|c|} \hline
score &50 \le x < 55 &55 \le x < 60 &60 \le x < 65 &65 \le x < 70 \\ \hline frequency &12 &19 &21 &15 \\ \hline \end {array} \)

The mean mark on a test is 10, with a standard deviation of 1.2. Find the percentage of students who achieved a mark greater than 11.2.

Find the mean if a score of 5.6 has a \(z\)-score 0.5 when the standard deviation of the scores is 2.2.

In which of the following subjects did John achieve his best result?

\( \begin {array} {|c|c|c|} \hline
subject & mean & standard \ deviation & Kate’s \ time \\ \hline
chemist & 60 & 3 & 54 \\ \hline
economy & 63 & 2 & 55 \\ \hline
finance & 64 & 4 & 58 \\ \hline
geography & 65 & 5 & 57 \\ \hline
\end{array} \)

Describe the strength of the linear relationship with correlation coefficient \(r = 0.9\).