Question

In a survey of 1080 ​people, 766 people said they voted in a recent presidential election. Voting records show that 68 ​% of eligible voters actually did vote. Given that 68 ​% of eligible voters actually did​ vote,

(a) find the probability that among 1080 randomly selected​ voters, at least 766 actually did vote.​

(b) What do the results from part​ (a) suggest? ​(a) ​P(X greater than or equals 766​)=

Answer 1

Using Normal approximation to Binomial

Mean = n * P = ( 1080 * 0.68 ) = 734.4
Variance = n * P * Q = ( 1080 * 0.68 * 0.32 ) = 235.008
Standard deviation = = 15.33

P ( X >= 766 )
Using continuity correction
P ( X > n - 0.5 ) = P ( X > 766 - 0.5 ) =P ( X > 765.5 )

P ( X > 765.5 ) = 1 - P ( X < 765.5 )
Standardizing the value

Z = ( 765.5 - 734.4 ) / 15.33
Z = 2.03

P ( Z > 2.03 )
P ( X > 765.5 ) = 1 - P ( Z < 2.03 )
P ( X > 765.5 ) = 1 - 0.9788
P ( X > 765.5 ) = 0.0212

Part b)

The given probability 0.0212 is less than 5% i.e 0.05, hence it is unusual event.