New Toy The team has been in operation and has met success. The team has 10 site

Question

New Toy The team has been in operation and has met success. The team has 10 sites that are selling the wooden wagons per the team's engineering plan. The team now wishes to determine if another wooden toy can successfully be introduced. The team has considered a wooden duck. After examining the operations to construct the duck, the team has decided that the duck would need to sell at 30% of the volume of wagons sold. If the duck sold at 10% then the team would not have enough profit to justify building the duck. The team is fairly optimist that the duck will be successful. The team estimates the probability to be.60 for success with the duck. The team has decided to use Bayes and the binomial distribution to test this 60% success prediction. The team chose 6 of the customer sites to test market the duck. Build a table giving the posterior probabilities for 0, 1, 2, 3, 4, or 5 successful sites. For each set of sales figures, give the probability for success of the new toy. How many sites must come back positive for the team to have the team's 60% probability of success?

Explanation / Answer

As team is fairly optimist that the probbability for success of duck = 0.60

Now sample size = 6

Here posterior probability means that we are counting the null hypothesis true. that means p = 0.6

Here thwe table giving posterior probability for 0,1,2,3,4 and 5 sites.

Here P(x) is the probability of success of X toy and p(x) is the probability of success of the new toy.

So, as we can see that for X = 4 ; P(X) > 0.60 so we can say that there must be atleast 6 sites that shall come positive for the team to have 60% probability of success.

x p(x) P(X) 0 0.0041 0.0041 1 0.0369 0.0410 2 0.1382 0.1792 3 0.2765 0.4557 4 0.3110 0.7667 5 0.1866 0.9533

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