Solution Found!
Solved: Consider the next 1000 95% CIs for ? that a
Chapter 7, Problem 11E(choose chapter or problem)
Problem 11E
Consider the next 1000 95% 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? What is the probability that between 940 and 960 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?]
Questions & Answers
QUESTION:
Problem 11E
Consider the next 1000 95% 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? What is the probability that between 940 and 960 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?]
ANSWER:
Step 1 of 2
Given that the solution has 1,000 trials and the probability of success is 0.95 which is the same for all the trials.
Also, there are 1,000 CI’s that are independent of each other.
The random variable 
Then the expected number of captures is given by,
Therefore, the expected number of captures corresponding to 