The mean of a set of five scores is \( 68 \). What is the new mean of the set of scores after a score of \( 20 \) is added?

A restaurant makes sales with the median is 210 dollars and the mean is 165 dollars. Which is the best measure of centre use it to predict average profit?

Use the scatter plot to predict the age of a child who is 55 kg.

Predict \(y\) when \(x = 8\)

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.

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

When estimating a value within the range of collected data, this is called interpolation and the estimate is quite reliable.

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?

The mean mark on a test is 60, with a standard deviation of 2. Find the percentage of students who achieved a mark greater than 43.

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

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

For normally distributed data \(X \sim N\left( {25,{3^2}} \right)\), find the value of \(k\) for \(\Pr \left( {X < k} \right) = 0.348\), correcting to two decimal places.