Math Problem Statement
Set up the calculator’s random number generator to “simulate” tossing a coin 25 times. The easiest way to do this is to generate 0's and 1's, with 1 representing heads and 0 representing tails. To populate LIST1 with trials use randInt(0,1,25) to generate a list of 0’ and 1’s that are stored in list 1. That is…DEFINE L1 as randInt(0,1,25). (RandInt is found under MATH > PRB>#5.) By adding up all the 0's and 1's you can effectively count the number of heads. (2 nd List, MATH, SUM (L1). Dividing that count by the number of tosses will get you the sample proportion of heads. Enter that into the percent column and repeat this 19 more times. RECORD the results in table form. Table should have 3 columns and 20 rows
Repeat steps 1 – 3…this time tossing the coin 100 times for a total of 20 trials
. Compare your two distributions of the proportions of heads observed from the 25 tosses and the 100 tosses.
Solution
I’ve displayed two tables representing the results of 20 trials for each coin toss simulation, with one table showing proportions of heads for 25 tosses per trial and the other for 100 tosses per trial. These tables allow you to observe the variations in the sample proportion of heads across trials for both 25 and 100 coin tosses. Comparing these can reveal the stability of the observed proportions as the number of tosses increases.
Would you like a deeper analysis of the distributions, or do you have any specific questions?
Here are some follow-up questions:
- How does increasing the number of tosses affect the variability of the sample proportion of heads?
- What conclusions can you draw about the distribution shape when tossing the coin 100 times compared to 25 times?
- How closely do the proportions in each trial approach 0.5, and does the approach differ with more tosses?
- What other statistical measures could help analyze the consistency between these two sets of trials?
- Would repeating this experiment further help confirm your observations?
Tip: The Law of Large Numbers states that as the sample size grows, the sample mean will tend to get closer to the expected value.
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Math Problem Analysis
Mathematical Concepts
Probability
Random Number Generation
Proportions
Statistics
Formulas
randInt(0,1,n): Generates a list of random 0s and 1s
Sum(L1): Sums values in a list to count occurrences of 1 (heads)
Proportion of Heads = Sum of Heads / Total Number of Tosses
Theorems
Law of Large Numbers
Suitable Grade Level
Grades 9-12