Which of the following would result in a better representation of data that could also use a binomial distribution model?(1 point)

Question

Responses

a sample of 1,000 people to represent a population of 11,000
a sample of 1,000 people to represent a population of 11,000

a sample of 300 people to represent a population of 700
a sample of 300 people to represent a population of 700

a sample of 100 people to represent a population of 200
a sample of 100 people to represent a population of 200

a sample of 500 people to represent a population of 800
a sample of 500 people to represent a population of 800

Answer 1

To determine which sample size would result in a better representation of data that could use a binomial distribution model, we should consider the ratio of the sample size to the population size. A better representation is typically indicated by a larger sample size relative to the population size.

Let's evaluate the options given:

1. A sample of 1,000 people to represent a population of 11,000
   Proportion: $\frac{1000}{11000}\approx 0.0909$

2. A sample of 300 people to represent a population of 700
   Proportion: $\frac{300}{700}\approx 0.4286$

3. A sample of 100 people to represent a population of 200
   Proportion: $\frac{100}{200}=0.5$

4. A sample of 500 people to represent a population of 800
   Proportion: $\frac{500}{800}=0.625$

Based on the proportions calculated, we can see that:

• The sample of 100 out of 200 has a 50% proportion.
• The sample of 300 out of 700 has about a 42.9% proportion.
• The sample of 500 out of 800 has a 62.5% proportion.
• The sample of 1,000 out of 11,000 has about 9.1% proportion.

The best representation in terms of sample size relative to population size is:

D. a sample of 500 people to represent a population of 800 (0.625)

This option has the highest proportion of sample size to population size, resulting in a better representation of data that could use a binomial distribution model.