Question

In a survey of 1396 people, 1023 people said they voted in a recent presidential election. Voting records show that 71% of eligible voters actually did vote. Given that 71% of eligible voters actually did vote, (a) find the probability that among 1398 randomly selected voters, at least 1023 actually did vote. (b) What do the results from part (a) suggest?

A. P(X≥1023)=0.023; The results suggest that the observed voter turnout is significantly lower than expected.
B. P(X≥1023)=0.977; The results suggest that the observed voter turnout is significantly higher than expected.
C. P(X≥1023)=0.977; The results suggest that the observed voter turnout is similar to the expected turnout.
D. P(X≥1023)=0.023; The results suggest that the observed voter turnout is similar to the expected turnout.

Answer 1

To find the probability of at least 1023 people voting out of 1398 randomly selected voters, use the binomial distribution formula. The observed voter turnout is significantly higher than expected.

Step-by-step explanation:

a. To find the probability that at least 1023 people actually voted out of 1398 randomly selected voters, we need to use the binomial distribution formula: P(X ≥ k) = 1 - P(X < k-1). In this case, k = 1023. We can calculate P(X < 1023) using the binomial distribution formula with n = 1398, p = 0.71, and x = 1022. Then, we subtract this value from 1 to find the probability that at least 1023 people voted: P(X ≥ 1023) = 1 - P(X < 1023). Plug in the values and calculate the probability.

b. The result from part (a) suggests that the observed voter turnout is significantly higher than expected, as the probability of at least 1023 people actually voting is high.