Problem 1: A coin is unbalanced such that it comes up tails 55% of the time. In an effort to prove that the coin is unfair, an experimenter flips the coin 50 times.

a) What is the probability that the coin comes up tails more than 25 times?

b) What is the probability that the coin comes up tails more than 30 times?

c) What is the probability that the coin comes up tails exactly 25 times?

Problem 2: A can of Pepsi is supposed to contain, on the average, 12 ounces of soda with a standard deviation of 0.3 ounces. Suspecting fraud, you take a random sample of 40 cans and measure the amount of Pepsi in each. Your measurements show that the 40 cans had a mean of 11.9 ounces. What is the probability of a random sample of 40 cans having a mean of 11.9 ounces of soda or less?

Problem 3: What are the conditions necessary for using the formula for standard deviation sigma = Sqrt( (P*(1-p) / n) when examining a population from a sampling distribution?