1 What does the random variable for a binomial experiment of n trials me 2. What
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1 What does the random variable for a binomial experiment of n trials me 2. What does it mean to say that the trials of an experiment are independent? 3. For a binomial experiment, how many outcomes are possible for each trial? What are the le outcomes? In a binomial experiment, is it possible for the probability of success to change form one trial to the next? Explain. 4. In an experiment, there are n independent trials. For each trial, there are three outcomes, A, B, and C. For each trial, the probability of outcome A is 0.40; the probability of outcome B is 0.5; and the probability of outcome C is 0.10. Suppose there are 10 trials. a) Can we use the binomial experiment model to determine the probability of four outcomes 5. of type A, five of type B, and one of type C? Explain. Can we use the binomial experiment model to determine the probability of four outcomes of type A and six outcomes that are not of type A? Explain. What is the probability of success on each trial? b) carnival game, there are six identical boxes, one of which contains a prize. A ize is 6. In a certain contestant wins the prize by selecting the box containing it. Before each game, the old pr removed and another prize is placed at random in one of the six boxes. Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game five times wins exactly twice? Check each of the requirements of a binomial experiment and give the values of n,r, and p 7, According to the college registrar's office, 40% of students enrolled in an introductory statistics class this semester are freshmen, 25% are sophomores, 15% are juniors, and 20% are seniors. You want to determine the probability that in a random sample of five students enrolled in introductory statistics this semester, exactly two are freshmen. a) Describe a trial. Can we model a trial as having only two outcomes? If so, what is success? What is failure? What is the probability of success? b) We are sampling without replacement. If only 30 students are enrolled in introductony statistics this semester, is it appropriate to model 5 trials as independent, with the same probability of success in each trial? Explain. What other probability distribution would be more appropriate in this setting?Explanation / Answer
1)A binomial random variable measures the number of successes in N trials of a binomial experiment.
2)Independent means that the probability throughout the experiment for any trial should be constant.
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