Question

In a survey of 1168 ​people, 741 people said they voted in a recent presidential election. Voting records show that 61​% of eligible voters actually did vote. Given that 61​% of eligible voters actually did​ vote, (a) find the probability that among 1168 randomly selected​ voters, at least 741 actually did vote.​ (b) What do the results from part​ (a) suggest?

Answer 1

Here we are given n= 1168, p = 0.61 ,
= n*p = 1168 * 0.61 = 713.48, nq = 1168 * 0.39 = 455.52

Here both np and nq are greater than 5 , we here we use normal approximation to Binomial distribution.

A) p ( x 741 ) = 1 - p ( x < 741 )

                        =

                        = 1 - p ( z < 1.65 )

                       = 1 - 0.9505

                       = 0.0495

B) Here the probability that among 1168 randomly selected​ voters, at least 741 actually did vote 0.0495, which is very less. This suggest that there is very less chance that among 1168 randomly selected​ voters, at least 741 actually did vote. Actually voted voters may be less than 741

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