6. [-/2 Points] DETAILS MY NOTES DEVORESTAT9 7.1.011.5. ASK YOUR TEACHER PRACTICE ANOTHER Consider the next 1000 98% CIs for $\mu$ that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of $\mu$? USE SALT intervals What is the probability that between 970 and 990 of these intervals contain the corresponding value of $\mu$? [Hint: Let Y = the number among the 1000 intervals that contain $\mu$. What kind of random variable is Y?] (Use the normal approximation to the binomial distribution. Round your answer to four decimal places.)
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Step 1: Since the confidence level is 98%, we expect 98% of the intervals to capture the true value of μ. Show more…
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Consider the next 1000 80% CIs for μ that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ? intervals What is the probability that between 790 and 810 of these intervals contain the corresponding value of μ? [Hint: Let Y = the number among the 1000 intervals that contain μ. What kind of random variable is Y?] (Use the normal approximation to the binomial distribution. Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.
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In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you take the free samples offered in supermarkets? About 58% of all customers will take free samples. Furthermore, of those who take the free samples, about 41% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 309 customers passed by your counter. (Round your answers to four decimal places.) (a) What is the probability that more than 180 will take your free sample? (b) What is the probability that fewer than 200 will take your free sample? (c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample) = 0.41, while P(sample) = 0.58. (d) What is the probability that between 60 and 80 customers will take the free sample and buy the product? Hint: Use the probability of success calculated in part (c).
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