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Binomial Experiments
Which of the following are binomial experiments?
Can any that are not be modified so that they
will become binomial experiments?
a)
Richard has just been given a 10question multiplechoice quiz in his history class.
Each
question has 5 possible responses, only one of which is correct.
Since Richard has not attended
class recently, he does not know any of the answers.
Assuming that Richard guesses on all 10
questions, is this a binomial experiment?
i)
The experiment consists of 10 trials. Each trial consists of Richard’s randomly guessing the
answer to one of the questions.
ii)
The trials are independent of each other due to random guessing – whether his guess is
correct on one question gives no information about whether his guess is correct on any other
question.
iii)
Each trial has two possible outcomes:
Success = {Richard guesses the correct answer to the
question} or Failure = {Richard does not guess the correct answer to the question}.
iv)
P(Success) = 0.20 for each trial, since Richard is randomly picking one of the 5 possible
responses to each question.
Yes, this is a binomial experiment, with n = 10 and p = 0.20.
b)
One hundred consumers are surveyed to determine whether they like Sudsy Soap.
i)
The experiment consists of 100 trials.
Each trial consists of asking one consumer whether he/
she likes Sudsy Soap.
ii)
We cannot say that the trials are independent of each other.
Why?
iii)
Each trial has two possible outcomes:
Success = {the consumer says that he/she does like
Sudsy Soap} or Failure = {the consumer says that he/she does not like Sudsy Soap}.
iv)
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 Fall '10
 Staff
 Statistics, Binomial

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