Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 8 Probability and Statistics
Problem
Solution
1) A basketball player attempted 1789 free throws. He made 801 of them. What is the probability that the player will make the next shot he attempts? Write the probability as a decimal rounded to the nearest thousandth. Probability = 801 / 1789 = 0.44577 = 0.448

2) Elite Style inspects 500 hair dryers manufactured and finds 495 to have no defects. There are 20,000 hair dryers in their warehouse. Predict the number of hair dryers in the warehouse that will have no defects. 		(495 / 500) x 20,000 = 19,800

3) A data set consists of seven different positive whole numbers. The mean of the data is 76. What is the largest possible median of the data?
  1. For the median to be maximum, the 3 numbers below it must be as small as possible = 1,2 and 3
  2. The 7 members of the data set must sum to 76x7 = 532, so the median and the 3 numbers above it must sum to 532 - 6 = 526
  3. For the median to be maximum, the median and the 3 numbers above it must be as high as possible, so if they are all different they must be 130, 131, 132 and 133, so the highest median is 130
  4. As a check:
    (1+2+3+130+131+132+133)/7 = 532/7 = 76

Problem
Solution
4) Hannah has a bag of marbles. 13 are yellow, 16 are green, 23 are red, 8 are blue, and 6 are multicolored. The multicolored marbles are red and blue. If Hannah randomly selects a marble, what is the probability that the marble will have red or blue in it? Express your answer as a ratio.
  1. There are 13+16+23+8+6 = 66 marbles in the bag.
  2. Probability = probability of a red marble + probability of a blue marble =
    (23+6)/66 + (8/66) = 37/66

5) The histogram shows the number of hours students in Mrs. Bell's business class average at their part-time jobs. What is the probability that a student randomly selected from the business class works 5-10 hours per week?
  1. Total number of students (add up the heights) =
        4+9+5+2 = 20 students
  2. Probability that student works 5-10 hours (second bar) = 9/20 = 0.45 or 45%