Question: (18 pts) Supreme Chocolate claims its ice cream tastes so good you can distinguish it from all other brands of chocolate ice cream! Five different brands of chocolate ice cream (one of them Supreme Chocolate) are set before six students who are to pick the one that tastes the best. Assume there is really no difference in the way any of these ice creams taste. However, each student picks one ice cream anyway, not knowing which brand it is because all ice creams are presented in identical dishes without brand labels.

a.) Argue that this is a binomial experiment.

b.) State the n, p and q for this experiment.

c.) State the random variable for this experiment.

d.) What is the probability that none of the students choose Supreme Chocolate?

e.) What is the probability that at least three students choose Supreme Chocolate?

f.) What is the probability that all six students choose Supreme Chocolate?

g.) If all six students choose Supreme Chocolate, might this indicate that the given assumption of no difference in taste may be false? Explain.

h.) Find the mean for this experiment.

i.) Find the standard deviation for this experiment.