Question

In a survey of 1394 people, 928 people said they voted in a recent presidential election. Voting records show that 64% of eligible voters actually did vote. Given that 64% of eligible voters actually did vote, (a) find the probability that among 1394 randomly selected voters, at least 928 actually did vote. (b) What do the results from part (a) suggest?

(a) P(X ≥ 928) = (Round to four decimal places as needed.)
(b) What does the result from part (a) suggest?
A. People are being honest because the probability of P(x ≥ 928) is at least 1%.
B. Some people are being less than honest because P(x ≥ 928) is less than 5%.
C. People are being honest because the probability of P(x ≥ 928) is less than 5%.
D. Some people are being less than honest because P(x ≥ 928) is at least 1%.

Answer 1

To find the probability that at least 928 people actually voted out of 1394 randomly selected voters, we need to use the binomial distribution. The result suggests that people are being honest because the probability of at least 928 people voting is at least 1%.

Step-by-step explanation:

To find the probability that at least 928 people actually voted out of 1394 randomly selected voters, we need to use the binomial distribution. The formula for the probability of x or more successes in n trials is:

P(X ≥ x) = 1 - P(X < x)

Given that 64% of eligible voters actually voted, the probability of one voter actually voting is 0.64. So the probability of at least 928 people voting out of 1394 is:

P(X ≥ 928) = 1 - P(X < 928)

P(X < 928) = (0.64)^928 * (1-0.64)^(1394-928) * combination(1394, 928)

By subtracting this probability from 1, we can find the probability of at least 928 people voting. You can use a calculator or statistical software to calculate the actual probability.

The result from part (a) suggests that people are being honest because the probability of at least 928 people voting is at least 1%.