Applications using Sample Proportions Preview CT-STEM

Apply - evaluate claims using the sampling distribution

Below are a few additional questions related to sampling distributions for proportions. These are the sorts of questions that you'll be expected to answer on an AP test. Be sure to check all necessary conditions and show all work. Do your work on paper and upload a scanned image for the questions below. See the example below for what an exemplary response looks like for these types of problems.

Example problem and solution: Suppose it is known that 21% of all Skittles produced are yellow. We will also assume that every bag of Skittles is a simple random sample from that entire population. Suppose you purchase a bag containing 120 Skittles. What is the probability of that bag containing 30 or more yellow Skittles?

Questions

Please answer the questions below.

Question 3.1

In a congressional district, 55% of registered voters are Democrats. Suppose we take a random sample of 100 voters from this congressional district. What is the probability of getting less than 50% Democrats in a random sample of size 100?

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Question 3.2

In July 2020, the Chicago Tribune asked a random sample of 750 Chicago residents. "Do you wear a face covering in public?" Based on a previous study by the IDPH, we know that 50% of ALL Chicago residents actually wear a face covering in public. Let \(\hat p\) be the sample proportion who say that they wear a face covering in public. What is the probability that, in a random sample of 750, more than 75% will respond "Yes (I wear a face covering in public)"?

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Notes

These notes will appear on every page in this lesson so feel free to put anything here you'd like to keep track of.