The following data give the ages (in years) of all six members of a family. 56 50 31 27 22 12 List all possible samples of size five (without replacement) that can be selected from this population. Calculate the mean for each of these samples. Enter the exact answers. For a sample 56, 50, 31, 27, 22, x = i For a sample 56, 50, 31, 27, 12, x = i For a sample 56, 50, 31, 22, 12, x = i For a sample 56, 50, 27, 22, 12, x = i For a sample 56, 31, 27, 22, 12, x = i For a sample 50, 31, 27, 22, 12, x = i Write the sampling distribution of x. Find P(x = 28.4). Round your answer to three decimal places. P(x = 28.4) =

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### Sample Mean Calculation for a Family's Ages

The following data give the ages (in years) of all six members of a family:

\[ 56, 50, 31, 27, 22, 12 \]

You are asked to list all possible samples of size five (without replacement) that can be selected from this population and calculate the mean for each of these samples. Enter the exact answers.

#### Samples of Size Five:
1. **For a sample 56, 50, 31, 27, 22:**
   \( \bar{x} = \)
2. **For a sample 56, 50, 31, 27, 12:**
   \( \bar{x} = \)
3. **For a sample 56, 50, 31, 22, 12:**
   \( \bar{x} = \)
4. **For a sample 56, 50, 27, 22, 12:**
   \( \bar{x} = \)
5. **For a sample 56, 31, 27, 22, 12:**
   \( \bar{x} = \)
6. **For a sample 50, 31, 27, 22, 12:**
   \( \bar{x} = \)

#### Sampling Distribution
Write the sampling distribution of \( \bar{x} \). Then, find \( P(\bar{x} = 28.4) \).

Round your answer to three decimal places.

\[ P(\bar{x} = 28.4) = \]
Transcribed Image Text:### Sample Mean Calculation for a Family's Ages The following data give the ages (in years) of all six members of a family: \[ 56, 50, 31, 27, 22, 12 \] You are asked to list all possible samples of size five (without replacement) that can be selected from this population and calculate the mean for each of these samples. Enter the exact answers. #### Samples of Size Five: 1. **For a sample 56, 50, 31, 27, 22:** \( \bar{x} = \) 2. **For a sample 56, 50, 31, 27, 12:** \( \bar{x} = \) 3. **For a sample 56, 50, 31, 22, 12:** \( \bar{x} = \) 4. **For a sample 56, 50, 27, 22, 12:** \( \bar{x} = \) 5. **For a sample 56, 31, 27, 22, 12:** \( \bar{x} = \) 6. **For a sample 50, 31, 27, 22, 12:** \( \bar{x} = \) #### Sampling Distribution Write the sampling distribution of \( \bar{x} \). Then, find \( P(\bar{x} = 28.4) \). Round your answer to three decimal places. \[ P(\bar{x} = 28.4) = \]
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