Question

In a survey of 1073 ​people, 743 people said they voted in a recent presidential election. Voting records show that 66​% of eligible voters actually did vote. Given that 66​% of eligible voters actually did​ vote, (a) find the probability that among 1073 randomly selected​ voters, at least 743 actually did vote.​ (b) What do the results from part​ (a) suggest? ​(a) ​P(Xgreater than or equals743​)equals nothing ​(Round to four decimal places as​ needed.)

Answer 1

The number of people who voted out of 1073 is modelled as:

This can be approximated to a normal distribution as:

Therefore the required probability is now computed as:

Applying for continuity correction, we get here:

Converting it to standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.0135 is the required probability here.

b) As the probability is 0.0135 < 0.05, therefore we have sufficient evidence at 5% level of significance that actually less than 66% of the eligible voters actually did vote.