Probability Distribution ? HELP HELP

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The manufacurer wishes to copare the taste appeal of a new formula (formula B) with that of the standard formula (formula A) . Each of four judges is given three glasses in a random order, two containing formula A and the other containing formula B. Each judge is asked to state which glas he most enjoyed. suppose that two formulas are equally attractive. Let Y be the number of judges stating a preference for the new formula: a) Find the probability function for Y b) what is the probability that at least three of the four judges state a preference for the new formula? c) Find Expected values of Y d) Find the variance of Y

Racheeta · Sep 10, 2009 3:37 PM · 14,264 views

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If I have understood your question correctly it can be modeled with binomial distribution.  Part a). The probability function of Y is:f(y) = (n choose y)*p^y*(1-p)^(n-y) where 0 =< y =< 4, n = 4, and probability of choosing new formula (p) = 1/2 Part b). P( Y => 3) = 1 - P(Y =< 3) P(Y =< 3) = Summation {f(y)}  Part c). E(Y) is mean of Y and mean of binomial distribution is n*p E(Y) = np Part d). Variance of binomial distribution is n*p*(1-p) Now you plug in the numbers and you should get the answers. I hope that helps... good luck with that!

geico · Sep 10, 2009 7:29 PM

Thank you so much.. I've one confusion here. isn't the probability of choosing new formula would be 1/3 instead of 1/2 ? Thanks.

Racheeta · Sep 12, 2009 5:16 PM

I also think that probability of new formula is 1/3, (one new formula and 2 old one)

khoi_k_khoi_k · Sep 12, 2009 5:45 PM

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