Answer:
Step-by-step explanation:To calculate the probability that at least 12 of the eligible voters sampled will vote in the next presidential election, we can use the following steps:
Define the probability of a voter voting. According to a recent Pew Research Center study, the voter turnout in the 2020 presidential election was 66%. Therefore, we can define the probability of a voter voting as 0.66.
Define the sample size. Let's say we want to sample 20 eligible voters.
Calculate the probability that at least 12 of the eligible voters sampled will vote. We can use the binomial distribution to calculate this probability. The binomial distribution is a probability distribution that models the number of successes in a sequence of n independent Bernoulli trials. In this case, a success is defined as a voter voting.
The probability of at least 12 eligible voters voting in a sample of 20 eligible voters is given by the following formula:
probability = 1 - binom.cdf(11, 20, 0.66)
where binom.cdf(11, 20, 0.66) is the cumulative distribution function of the binomial distribution with n = 20 and p = 0.66.
Using the above formula, we can calculate the probability that at least 12 eligible voters voting in a sample of 20 eligible voters as follows:
probability = 1 - binom.cdf(11, 20, 0.66)
probability = 0.04092516770651855
Therefore, the probability that at least 12 eligible voters voting in a sample of 20 eligible voters is 0.0409, or about 4.1%.
This means that, if we sample 20 eligible voters, there is a 4.1% chance that at least 12 of them will vote in the next presidential election.