For this problem, you must use the equation for the binomial distribution (i.e., do not use BINOMDIST or binomial tables). You may check your results with BINOMDIST, but you must submit your work showing the proper use of the binomial equation. The Excel function FACT returns the factorial of any given number. Recall that the binomial distribution was given in the notes as:
Each of six randomly selected beer drinkers is given a glass containing beer brand "S" and one containing beer brand "F". The glasses are identical in appearance except for a code on the bottom to identify the beer (a "blind taste test"). Suppose that there is actually no tendency among beer drinkers to prefer one beer to the other. Then p = P(selected individual prefers beer S) = 0.5, and X = number among the six who prefer beer S, where X is a binomial random variable.
a. What is the probability that at exactly 3 people prefer beer S? That is, find P(X = 3).
b. What is the probability that at least 3 people prefer beer S? That is, find P(X ≥ 3).