Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 5 Probability & Statistics
Problem
Hint
1) Restaurants often slip takeout menus under Rudy's apartment door. Rudy made a chart of how many menus were from each kind of restaurant. If this data is representative, then how many of the next 15 menus slipped under Rudy's apartment door will be Chinese? 1. The total number of menus Rudy received was _____.
2. Compute the fraction of the menus that are Chinese = _____
3. Apply this fraction to the next 15 menus = ____ menus.

2) Joey scores on 6 tests are:

    78, 86, 84, 74, 90, 92.

His teacher allowed him to correct his own tests and earn half of the points missed added on to his original test score. He did that for each one. By how much did his test average go up?		 1. Compute the average of Joey's scores = _____.
2. For each score,
    (1) subtract it from 100, and
    (2) divide by 2 and
    (3) add this to the original score.
3. Compute the average of his adjusted scores = ____.
4. Subtract the first average from this one = _____.

3) There are 10 green marbles and 2 blue marbles in a bag. Each day you select a blue marble you can stay up an extra half hour. Each time you select a green marble you have to go to bed at 9 pm. You select a marble without looking and then put it back. Over the course of 12 days how many days would you expect to go to bed after 9pm?		 1. There are a total of ____ marbles in the bag.
2. Compute the probability (fraction) of getting
    a blue marble = _____.
3. Apply this fraction to the total number of days = _____ days.

Problem
Hint

4) Mollie invents a new board game that uses the spinner shown and one 6 sided die. You roll first and then spin, then move your piece on the board according to the spinner. The spinner is divided into three equal sections. What is the probability that you will move forward an even number of spaces on your turn?
"Double your role" on the spinner means
"double the number on your die"		 Big hint! : If you double your roll the number you get will be even!
1. What fraction of the "Proceed normally" third of the spinner will result in an even number? _____.
2. That is _____ of the total spinner.
3. Add up these fractions (double your roll + ____ of the total spinner) = _____.

5) What number can you add to this data set to change the median by 3?

    15  21  25  41  46  54   54  62   65  86  93		 1. The current median is _____.
2. When you add a single number to the data set you will now have an even number of elements, so the average of your new number and the current median is the new median.
3. This is either 3 less or 3 more than the current median.
4. Find a number to add that does this = _____.