DATA: Heads= 50 Tails= 43

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 93 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 93 times as a class. Using the binomial formula, binomial table, or your graphing calculator, calculate the probability that exactly 20 of our trials landed on heads. In other words, find P(20). Hint 1: Use Binompdf(n, p, x) Hint 2: Think in general for your probabilities (don't look at the outcomes of the class for the probabilities), when you flip a coin, what is the probability(p) of landing on heads?

3) In your calculations for question 2, what were the values of n, p, and q?

4) A coin is flipped 93 times, find the probability that fewer than 20 of the flips landed on heads. Hint: use Binomcdf(n,p,x)

5) A coin is flipped 93 times, find the probability that more than 20 of the flips landed on heads.

6) A coin is flipped 93 times, find the probability that the number of flips landing on heads is between 20 and 30 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 93 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.