Hello,
In a class of 24 students, every student flips fairly two coins 40 times each and records the results. Assume that the class obtained the expected results when they conducted the experiment.
a. Make a bar graph illustrating the combined class results
b. explain why an individual student's results might be different from the class results.
I'm really unsure where to begin. This is a review for our state test and it makes me nervous.
a. The combined class results should be 50% heads and 50% tails. Best I can tell, your bar graph would have only 2 bars, both at 50%.
b. The law of large numbers basically says that the more times a probabilistic event is attempted, the closer the outcome (empirical probability) will come to the predicted outcome (theorectical probability). So the class's 480 tosses is more likely to hit the expected 50/50 ratio of heads to tails than is an individual student's 40 tosses, due solely to chance ("random fluctuations").
Esye
Hello! I'm here to help you with your question and ease your nervousness. Let's break it down step by step so you can understand and answer the question confidently.
a. To make a bar graph illustrating the combined class results, you need to determine the possible outcomes when flipping two coins and record the frequency of each outcome.
Since each student flips two coins 40 times, there are 80 coin flips per student. With two possible outcomes for each coin flip (heads or tails), there are a total of 2^80 possible outcomes for 80 coin flips.
However, you're told that the class obtained the expected results, which means the outcomes were evenly distributed. In this case, there are three possible outcomes for each student:
1. Both coins showing heads
2. Both coins showing tails
3. One coin showing heads and the other showing tails
Now, you can create a bar graph with the three outcomes on the x-axis and the frequency on the y-axis, representing the combined class results.
b. An individual student's results might differ from the class results due to several factors:
1. Randomness: Flipping coins is a random process, and even with a fair coin, the actual results can deviate from the expected results. This is known as natural variation or chance.
2. Sampling error: An individual student's results can be influenced by the small sample size of 40 coin flips. With a larger sample size, the individual results would likely converge to the expected values.
3. Bias or systematic error: If an individual student has a biased coin or a biased flipping technique, their results would deviate from the expected values. Bias can occur due to various reasons, such as uneven weight distribution in a coin or a consistent flipping motion.
Remember, it's important to understand the concept rather than memorizing it for a test. By explaining these concepts in your own words, you'll solidify your understanding and be able to answer similar questions confidently. Good luck with your state test preparation!