Independent events Based on a Pitney Bowes survey, when 1009 consumers were asked if they are comfortable with drones delivering their purchases, 42% said yes. Consider the probability that among 30 different consumers randomly selected from the 1009 who were surveyed, there are at least 10 who are comfortable with the drones. Given that the subjects surveyed were selected without replacement, are the 30 selections independent? Can they be treated as being independent? Can the probability be found by using the binomial probability formula? Explain.

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Independent events Based on a Pitney Bowes survey, when 1009 consumers were asked if they are comfortable with drones delivering their purchases, 42% said yes. Consider the probability that among 30 different consumers randomly selected from the 1009 who were surveyed, there are at least 10 who are comfortable with the drones. Given that the subjects surveyed were selected without replacement, are the 30 selections independent? Can they be treated as being independent? Can the probability be found by using the binomial probability formula? Explain.

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Step 1

5% guideline for cumbersome calculations:

When sampling is done without replacement and the sample size is not more than 5% of the size of the original population, then the sample selections can be treated as a sampling with independent selections.

Step 2

A sample of 30 consumers is selected at random w...

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