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Q. 105

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The Practice of Statistics for AP Examination

Found in: Page 430

Book edition 6th

Author(s) Daren Starnes, Josh Tabor

Pages 837 pages

ISBN 9781319113339

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Short Answer

$10 %$ 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 $N$ ?

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Informaiton

The given population is 10%

Step 2: 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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