Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 8 Probability and Statistics
Problem
Hint
1) Roy is looking forward to making some good money once he's in high school. He does an informal survey of his older brother's friends. He puts the results of his survey in a table shown below. Compute the mean and median hourly wage for Roy's informal survey. Is Roy more likely to get a job that pays close to the mean hourly wage or to the median hourly wage? Explain.
  1. Compute the median:
    There are ___ measurements, so the median is the middle one counting from either end = ______
  2. The mean is the sum of all the wages divided by the number of measurements

    = _______
  3. Roy is most likely to get the ______ because



2) Here's a game with one standard six sided die with the numbers 1 - 6. In at most three rolls of the die be the one to get as close to 10 as possible without going over. If you roll a 4 on the first roll, what's the probability you will go over 10 in the next two?
  1. If you roll a 4 on the first die, then any roll over ____ will go over 10.

  2. If you look at the sum of 2 dice table to the right, there are ____ 2-dice sums that result in _____ or more, so the probability that you will go over is _______

Problem
Hint
3) College bound high school students often take a foreign language. One school has a senior class of 255 students. 178 are college bound and they all take either French or Spanish. 97 students have taken at least 3 years of high school French, and 123 have taken at least 3 years of high school Spanish. No student has taken at least 3 years of both languages. If a student is selected at random, what's the probability they've had at least three years of French or Spanish but are not college bound?
  1. There are ______ students that are not college bound.

  2. There are a total of _____ students that have taken at least 3 years of French or Spanish and _____ of them are college bound, leaving _____ that have taken 3 years of a foreign language and are not college bound.

  3. The probability that a non-college-bound student takes 3 years of a foreign language is therefore

    _______________
4) A coin is weighted so that it comes up heads twice as often as tails. If it comes up heads 5 times in a row, what's the probability it will come up tails on the next toss? What's happened in the past doesn't affect what happens in the future for independent probabilities, so the probability of a tails is

______

5) Gavin had a GPA of 2.9 going into his last semester of 8th grade. He would like to bring it up to a 3.0 or higher. Each semester he has taken 6 classes and each one is worth 1 credit. His middle school is 6th through 8th for a total of 6 semesters. What's the lowest his last semester's GPA can be to get a cumulative GPA of 3.0?
  1. Gavin has averaged a GPA of 2.9 for ___ semesters.

  2. Using G for his last semester GPA, write the equation for the mean of his 6 semesters and set it equal to 3.0 and solve for G:


    G = _____