The Virginia Department of Health publishes COVID-19 vaccination data on their website. As of 10/5/2021, 60.6% of the population of Virginia is fully vaccinated. This rate varies drastically from county to county. Specifically, Fairfax County’s full vaccination rate is 74% and Lee County’s full vaccination rate is 40%. A researcher took a random sample of 14 individuals from Fairfax County and another random sample of 14 individuals from Lee County and asked them whether they could verify that they are fully vaccinated. Each sample was selected in a single day. 1. Calculate the mean and standard deviation of the number of individuals from Fairfax County and Lee County in this sample who are fully vaccinated. Show your work using the binomial mean and binomial standard deviation formulas and provide your two means and two standard deviations in your document. Round your answers to two decimal places. (It is not necessary to use StatCrunch for this part.)
The Virginia Department of Health publishes COVID-19 vaccination data on their website. As of 10/5/2021, 60.6% of the population of Virginia is fully vaccinated. This rate varies drastically from county to county. Specifically, Fairfax County’s full vaccination rate is 74% and Lee County’s full vaccination rate is 40%. A researcher took a random sample of 14 individuals from Fairfax County and another random sample of 14 individuals from Lee County and asked them whether they could verify that they are fully vaccinated. Each sample was selected in a single day.
1. Calculate the mean and standard deviation of the number of individuals from Fairfax County and Lee County in this sample who are fully vaccinated. Show your work using the binomial mean and binomial standard deviation formulas and provide your two means and two standard deviations in your document. Round your answers to two decimal places. (It is not necessary to use StatCrunch for this part.)
2. Calculate the probability that exactly seven of the 14 individuals from Fairfax County in this sample are fully vaccinated using the StatCrunch binomial calculator. Copy this image with values from StatCrunch into your document. Then, once you obtain your answer, round your answer to four decimal places and write a one sentence interpretation of the probability in context of the question.
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