Estimate the mean of the data.

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

Using the box-and-whisker plot for two singers A and B, who is more popular?

Find the interquartile range of the data represented in box-and-whisker plot.

\( \begin{array}{c|cccccc}
1 & 5 & 7 &&&& \\
2 & 0 & 3 & 6 & 9 && \\
3 & 1 & 1 & 4 & 7 && \\
4 & 6 & 7 &&&& \\
\end{array} \)

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

\(\begin{array} {|c|c|c|c|c|} \hline
score &20 \le x < 24 &24 \le x < 28 &28 \le x < 32 &32 \le x < 36 \\ \hline frequency &15 &15 &16 &17 \\ \hline \end {array} \)

Use technology to find the equation, \(y = mx + b\) of the linear regression for the data by considering any outliers. Express coefficients correct to two decimal places.

\( \begin{array}{|c|c|c|} \hline
x & 2 &7 &11 &18 &21 &25 &31 \\ \hline
y & 12 &14 &97 &121 &5 &24 &29 \\ \hline
\end{array} \)

A box contains balls numbered \( 1 \) to \( 50 \). One ball is taken randomly out of the box. Find the probability that it is a multiple of \( 12 \), given that it is a multiple of \( 3 \). Answer to two decimal places.

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

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

A new medicine for a certain disease is known to be successful in 75% of cases. Ten patients suffer take part in the testing of the medicine. Find the probability that all ten are cured, correcting to four decimal places.

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.

For normally distributed data \(X \sim N\left( {36,{4^2}} \right)\), find the value of \(k\) for \(\Pr \left( {36 – k < X < 36 + k} \right) = 0.427\), correcting to two decimal places.