Estimate the mean of the data.

\( \begin{array}{|c|c|c|c|c|c|} \hline
Class & 0 \le x < 50 & 50 \le x < 100 & 100 \le x < 150 & 150 \le x < 200 & 200 \le x < 250 \\ \hline Frequency (f) & 3 & 9 & 16 & 18 & 17 \\ \hline \end{array} \)

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

Find \( a, b, c \)   and the mean.

\( \begin{array}{|c|c|c|} \hline
Score (x) & Frequency (f) & f \times x \\ \hline
100 & 1 & 100 \\ \hline
200 & 6 & 1200 \\ \hline
300 & a & 2700 \\ \hline
400 & 7 & 2800 \\ \hline
500 & b & 1000 \\ \hline
Total & c & 7800 \\ \hline
\end{array} \)

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

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

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

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

Five per cent of items made by a factory machine are defective. The items are packed and sold in boxes of 20. Find the probability of at least one items being defective in a box, correcting to four decimal places.

A binomial random variable has a mean of 10 and a variance of 5. Find \(\Pr \left( {X = 3} \right)\), correcting to four significant figures.

Find the score if a \(z\)-score is 2.3 when the standard deviation is 5.1 and the mean is 55.

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

\( \begin {array} {|c|c|c|} \hline
subject & mean & standard \ deviation & John’s \ mark \\ \hline
chemist & 75 & 7 & 73 \\ \hline
economy & 70 & 6 & 73 \\ \hline
finance & 65 & 5 & 73 \\ \hline
geography & 80 & 8 & 73 \\ \hline
\end{array} \)