Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 8 Probability and Statistics
Problem
Hint
1) Kamal is throwing a dart at a circular dart board with radius 1 foot. His eyes are closed and it is just as likely the dart will strike one part of the board as another. What is the probability that the dart will stick closer to the edge than to the center? Compute the relative areas of a circular board with half the board radius to the whole board.
2) George has two counters in his pocket. They are the same size only one is red on both sides and one is red on one side and blue on the other. He pulls one counter out of his pocket without looking and puts it on the table. If the side showing is red, what is the probability that the other side is blue? The unseen 3 sides are _____, _____, and _____.

The probability of a blue side is _______

3) The lowest number in a set of five numbers is 10. The range is 60 and the mean is 40. What is the biggest the median could be?
  1. The highest number is _____ (10 + the range).
  2. In order to maximize the median, the second number must be equal to the lowest number and the higher missing number must be as low as possible without going below the median.
  3. For the mean to be 40, the median must be _____

Problem
Hint
4) CJ gets to pick out of the sticker jar as a reward for a job well done. Normally the sticker jar has a ratio of 5 smiley faces to 3 stars to 2 Hot Stuff stickers. Since he has to pick blind and really wants a Hot Stuff sticker he's disappointed to see that there are only 10 stickers left: 5 smiley faces and 5 stars. Ms. Andrews says she'll fill it up to 60 stickers before he picks and restore the ratio of 5:3:2. How many of each sticker will she add?
  1. There are a total of 5 + 3 + 2 parts of the 60 stickers.

  2. To restore the number of smiley faces she needs to add _____ smiley face stickers

  3. She needs to add ____ star stickers and

  4. _____ Hot Stuff stickers.
5) The table shows the average temperatures to the nearest tenth in Fahrenheit in Seattle over two five year spans, 1950-1954 and 2000-2004. Make a line graph of the differences between the 2000s data and the 1950s data on the provided axes on the answer sheet. What aspect of your line graph could you use to support global warming?

Subtract the 1950-1954 data points from the 2000-2004 data points and plot them.

I'll leave it to you to plot these points on the grid to the left!