1) Suppose you decide to analyse whether there is a significant relationship between the height and speed of long distance runners for your internal assessment exploration. To collect your data, you measure the heights of a sample of the runners on your school's boys and girls running teams and use the records from their races to find their average running times.

Assuming you found a statistical relationship showing that taller runners tended to run faster, determine which of the following statements is the most appropriate conclusion you could state.

2) A bag contains 1212 yellow and 88 purple marbles. Joe pays $2$2 for the opportunity to pick a marble from the bag. If he picks a yellow marble, he does not get anything. If he picks a purple marble, he gets $k.$k.

The game is fair. Find the value of k.k. Give an exact answer. Do not include the dollar sign in your answer.

3) In a school there are 200students. Out of these students, 80studyphysics, 90studybiology and 66donot study any of these two subjects.

A student is selected at random. Consider the following two events:

• B:the selected student studies biology
• P:the selected student studies physics

Determine if these events are independent or not. Write either "independent" or "not independent" as your answer.