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Chapter 7: Problem 56

Suppose that \(20 \%\) of the 10,000 signatures on a certain recall petition are invalid. Would the number of invalid signatures in a sample of 2000 of these signatures have (approximately) a binomial distribution? Explain.

Short Answer

Expert verified
Yes, the number of invalid signatures in a sample of 2000 of these signatures would have approximately a binomial distribution because the conditions of a binomial distribution are met.

Step by step solution

01

Identify the variables

The number of trials (n) is 2000 (the size of the sample), and the probability of success (p), which in this case represents an invalid signature, is given as 20% or 0.2.
02

Confirm if conditions of binomial experiment are met

The assumptions of a binomial distribution are: 1. There are only 2 outcomes (valid or invalid signature),2. The trials are independent (one signature does not affect the validity of the others), 3. The probabilities remain constant for all trials (20% is assumed to be the probability in all cases). The only assumption that might be questionable is the last one, as the proportion of invalid signatures may not be constant for every sample. But the problem statement suggests to consider the proportion as consistent.
03

Decide if the distribution is binomial

Given that the characteristics of a binomial distribution are satisfied in this problem, one can conclude that the number of invalid signatures in a sample of 2000 has approximately a binomial distribution.

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