Question

In a survey of 1440 ​people, 990 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 1440 randomly selected​ voters, at least 990 actually did vote.​ (b) What do the results from part​ (a) suggest?

Answer 1

It is given that the percentage of eligible voters actually did​ vote is 66%

Let p = proportion of eligible voters actually did​ vote = 0.66

Let X = number of eligible voters actually did​ vote .

Therefore X follows binomial distribution with parameters n = 1440 and p=0.66

Here we want to find P( X >= 990) = 1 - P( X < 990) = 1 - P( X <= 989) .....( 1 )

Let's used excel:

P( X <= 989) = "=BINOMDIST(989,1440,0.66,1)" = 0.9856

Plug this value in equation ( 1 ), so we get.

P( X < = 990) = 1 - 0.9856 = 0.0144

b) From part ( a) the probability of  at least 990 actually did vote is 0.0144 which is very small ( unusual) . So we can say that the data is not support the population from which sample is taken is that 66​% of eligible voters actually did vote