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 Probability Distribution ? HELP HELP
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Posted on 09-10-09 3:37 PM     Reply [Subscribe]
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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
 
Posted on 09-10-09 7:29 PM     Reply [Subscribe]
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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!
 
Posted on 09-12-09 5:16 PM     Reply [Subscribe]
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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.
 
Posted on 09-12-09 5:45 PM     Reply [Subscribe]
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I also think that probability of new formula is 1/3, (one new formula and 2 old one)
 

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