Bethel Does Flipping a Coin Represent a Binomial Experiment Probability Questions

Answer the following questions.

1. Does flipping a coin represent a binomial experiment? Let random variable X represent the number of times a coin lands on heads out of our 45 trials. Fully explain by referencing the conditions required for a random variable to follow a binomial distribution.
2. In our experiment we have tossed the coin 45 times as a class. Using the binomial formula, binomial table, or your graphing calculator, calculate the probability that exactly 3 of our trials landed on heads. In other words, find P(3)$$ $$
3. In your calculations for question 2, what were the values of n, p, and q?
4. A coin is flipped 45 times, find the probability that fewer than 12 of the flips landed on heads.
5. A coin is flipped 45 times, find the probability that more than 20 of the flips landed on heads.
6. A coin is flipped 45 times, find the probability that the number of flips landing on heads is between 5 and 10 inclusively.
7. We have discussed the formulas used to calculate the mean, variance, and standard deviation of a binomial random variable. Let random variable X represent the number of times a coin lands on heads out of our 45 trials. Calculate the mean and standard deviation of X.
8. For the events defined in questions 2, 4, and 5 are any of these events considered unusual? Explain why or why not.
9. How many times did we actually observe the coin landing on heads in our class data? Heads and Tails data Explain why this number is not equal to half of the total? What was the proportion of outcomes landing on heads that we actually observed? What would we observe if we continued to flip the coin 1000 times? (Apply the Law of Large number