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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Asked Jan 11, 2020
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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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Expert Answer

Step 1

Given that,

Population =1009 consumers

Randomly selecting 30 by without replacement.

The 30 selections are not independent, because the selections are occur without replacement.

Step 2

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 considered as independent selections.

But here 30 consumers are randomly selected,

Statistics homework question answer, step 2, image 1
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Step 3

Hence, it is approximately 3% of the consumers are selected from the population.

Here, 3% is less than the 5% of the population, so the selection of this customers is considered as independent...

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