A coin is to be spun 25 times. Let x be the number of spins that result in heads (H). Consider the following rule for deciding w
hether or not the coin is fair: Judge the coin to be fair if 8 ≤ x ≤ 17. Judge the coin to be biased if either x ≤ 7 or x ≥ 18. a. What is the probability of judging the coin to be biased when it is actually fair?
Since we have a fixed number of trials (N = 25) and the probability of getting heads is always p = 0.05, we are going to treat this as a binomial distribution.
Using a binomial probability calculator, we find that the probability of obtaining heads from 8 to 17 times is 0.9567 given that the con is fair. The probability of obtaining any other value given that the coin is fair is going to be:
1 - 0.9567 = 0.0433
Since we are going to conclude that the coin is baised if either x<8 or x>17, the probability of judging the coin to be baised when it is actually fair is 4.33%
