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?

There is an 80% chance that Ben passes his driving test and a 90% chance that Amy passes hers. Find the probability that Amy passes.

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 the financial expectation of a ticket in a raffle.   The raffle has 500 tickets and there is one prize worth 200 dollars.

The number of apple inboxes is normally distributed with mean 121 and standard deviation 7. Between what numbers will be contents of 68% of the boxes lie?

Find the mean if a score of 124 has a \(z\)-score -1.6 when the standard deviation of the scores is 13.

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.

If two-thirds of all primary school teachers are women, find the probability that when 4 teachers are chosen at random there are at least one woman, correcting to four decimal places.