Consider the next 1000 98% CIs for u 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 u? n USE SALT Jintervals What is the probability that between 970 and 990 of these intervals contain the corresponding value of u? [Hint: Let Y = the number among the 1000 intervals that contain u. 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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**Educational Website Transcription:**

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**Understanding Confidence Intervals**

Consider the next 1000 **98% Confidence Intervals (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 \( \mu \)?

**[Button: USE SALT]**

**Expected number of intervals:**  
\[\_\_\_\_\_\_\_\_\_\]

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**Probability Calculation**

What is the probability that between 970 and 990 of these intervals contain the corresponding value of \( \mu \)?

*Hint:* Let \( Y \) be 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.)

**Probability:**  
\[\_\_\_\_\]

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Transcribed Image Text:**Educational Website Transcription:** --- **Understanding Confidence Intervals** Consider the next 1000 **98% Confidence Intervals (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 \( \mu \)? **[Button: USE SALT]** **Expected number of intervals:** \[\_\_\_\_\_\_\_\_\_\] --- **Probability Calculation** What is the probability that between 970 and 990 of these intervals contain the corresponding value of \( \mu \)? *Hint:* Let \( Y \) be 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.) **Probability:** \[\_\_\_\_\] ---
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