SOLUTION: A large retail chain sends out an ad about a new product to 15 million users on Facebook and asks them to like the message. Assume the probability that a user will like the message

Question 1189419: A large retail chain sends out an ad about a new product to 15 million users on Facebook and asks them to like the message. Assume the probability that a user will like the message (instead of ignoring it) is 0.00001.
A. State assumptions for a binomial distribution to apply for X = the number of likes the message will receive. Identify n and p for that distribution.
B. Suppose the assumptions are met. Find the mean and standard deviation of X.
C. Is it reasonable to approximate the binomial distribution with the normal one? Why? (Assume the assumptions are met.)

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
two outcomes, independent, unchanging probability, fixed number of trials.
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15000000*0.00001=150
so n=15,000,000 and p=0.00001
the mean is np=150
the variance is np(1-p)=150*0.99999=149.9985
sd= sqrt (V)=12.25
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np should be greater than 10, so yes, a normal approximation will work.
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