Estimate the mean of the data.

\( \begin{array}{|c|c|c|c|c|c|} \hline
Class & 200 \le x \lt 300 & 300 \le x \lt 400 & 400 \le x \lt 500 & 500 \le x \lt 600 & 600 \le x \lt 700 \\ \hline
Frequency (f) & 21 & 23 & 29 & 35 & 17 \\ \hline
\end{array} \)

Select the corresponding frequency table for the cumulative frequency graph shown.

Using the box-and-whisker plot, which is the better result?

Find the median of the scores.

\( \begin{array}{|c|c|} \hline
Score & Frequency \\ \hline
5 & 6 \\ \hline
6 & 7 \\ \hline
7 & 12 \\ \hline
8 & 4 \\ \hline
\end{array} \)

Find \( a, b, c, d, e, f, g \)   and the mean.

\( \begin{array}{|c|c|c|} \hline
Score (x) & Frequency (f) & f \times x \\ \hline
5 & a & 5 \\ \hline
10 & 9 & b \\ \hline
15 & c & 165 \\ \hline
20 & 15 & d \\ \hline
25 & e & 350 \\ \hline
Total & f & g \\ \hline
\end{array} \)

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

Find \(x:P\left( {X \ge x} \right) = 0.8\).

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

Daniel is a marathon runner. On the Olympic course in the northern hemisphere, the meantime is 2 hours 16 minutes with a standard deviation of 5 minutes. On the southern hemisphere, the meantime is 2 hours 20 minutes with a standard deviation of 4 minutes. In the northern hemisphere, Daniel’s time was 2 hours 18 minutes and in the southern hemisphere, his time was 2 hours 21 minutes. By writing these \(z\)-scores, determine the better performance.

For normally distributed data \(X \sim N\left( {25,{5^2}} \right)\), find the value of \(k\) for \(\Pr \left( {X > k} \right) = 0.58\), correcting to two decimal places.

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