A study records the reaction times of gamers and non-gamers. The box-and-whisker plots show the distributions.
There are 15 non-gamers whose reaction time was slower than 480 milliseconds. Find the number of non-gamers in the study.[1]
Compare the averages and the distributions of the gamers’ and non-gamers’ reaction times, using figures.[3]
Boxes X, Y and Z contain: X—2 black and 1 white ball; Y—1 black and 5 white balls; Z—2 black and 2 white balls. A fair die chooses X on 6, Y on 4 or 5, and Z on 1, 2 or 3. One ball is then selected. A black ball wins $10 and playing costs $2.
Complete a tree diagram showing the box and ball probabilities.[2]
Find the probability of winning the $10 prize.[2]
Find the expected amount gained or lost after playing 12 games.[2]
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Answer:(a)(i) \(60\) (ii) gamers faster and more consistent (b)(i) completed tree (ii) \(\frac5{12}\) (iii) \(\$26\) gained