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Chapter 6: Q. 105 (page 430)

10%condition To use a binomial distribution to approximate the count of successes in an SRS, why do we require that the sample size n be less than 10%of the population size N?

Short Answer

Expert verified

The sample size n must be smaller than 10% of the population size N.

Step by step solution

01

Given Informaiton

The given population is 10%

02

Simplificaiton

If the 10 % condition is met, a binomial distribution can be used to approximate the number of successes in a simple random sample. The 10% condition requires that the sample represents less than 10% of the population. Despite the fact that the sample size is far too tiny in comparison to the population, it is reasonable to infer that the trials of occurrences are independent. This suggests that the sample size n must be smaller than 10% of the population size N in this situation.

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