The United States Senate has 100 members. Suppose that there are 54 Republicans and 46 Democrats. A committee of 15 is selected at random. What is the expected number of Republicans on this committee? 8.1 What is the standard deviation of the number of Republicans on this committee? 3.726 X

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**The United States Senate: Probability and Statistics**

The United States Senate consists of 100 members. Suppose that there are 54 Republicans and 46 Democrats. When a committee of 15 members is selected at random, statistical calculations can determine the expected number and standard deviation of Republicans in this committee.

**Question 1: Expected Number of Republicans**

- The expected number of Republicans on this committee is 8.1.

- This figure is marked with a green check, indicating it is correct.

**Question 2: Standard Deviation of Republicans**

- The standard deviation of the number of Republicans on this committee is 3.726.

- This answer is marked with a red cross, indicating it is incorrect.

These computations involve principles of probability and statistics, which can be used to analyze selections in large groups with known proportions.
Transcribed Image Text:**The United States Senate: Probability and Statistics** The United States Senate consists of 100 members. Suppose that there are 54 Republicans and 46 Democrats. When a committee of 15 members is selected at random, statistical calculations can determine the expected number and standard deviation of Republicans in this committee. **Question 1: Expected Number of Republicans** - The expected number of Republicans on this committee is 8.1. - This figure is marked with a green check, indicating it is correct. **Question 2: Standard Deviation of Republicans** - The standard deviation of the number of Republicans on this committee is 3.726. - This answer is marked with a red cross, indicating it is incorrect. These computations involve principles of probability and statistics, which can be used to analyze selections in large groups with known proportions.
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