Let’s say we want to know what percentage of people in the population are left-handed. It would be impossible to measure every single person in the world, so we take a sample of 500 people and create a proportion. In our sample, 75 people are left handed. So:

Figure 1. |
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We can find out the distribution of the sample proportion if our sample size is less than 5% of the total population size.

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Let's describe the sampling distribution: In a sample of 500 individuals, 75 are left handed. Describe the distribution of the sample proportion:

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First, we answer the two questions to verify that we can create a meaningful sampling distribution. After we find that the two requirements are met, we find a mean proportion of 0.15, with a standard deviation of 0.016.

Figure 4. |
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Using this information, we can finally create the distribution shown above.