Question

In a survey of 1359 ​people, 954 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 1359 randomly selected​voters, at least 954 actually did vote.​ (b) What do the results from part​ (a) suggest?

​(a) ​P(X ≥ 954​) = ? ​(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 ≥ 954​) is at least​ 1%.

B.People are being honest because the probability of P(x ≥ 954​) is less than​ 5%.

C.Some people are being less than honest because P(x≥954​) is at least​ 1%.

D.Some people are being less than honest because P(x≥954​) is less than​ 5%.

Answer 1

68% of eligible voters voted       
p = 0.68       
q = 1 - p = 1 - 0.68 = 0.32       
Let X be the number of voters who actually voted from the sample of 1359 voters       
X follows Binomial distribution with n = 1359 and p = 0.68       
        
a) P(X ≥ 954) = 1 - P(X < 954)       
= 1 - P(X ≤ 953)      
   We use Excel function BINOM.DIST to find the probability     
                = 1 - BINOM.DIST(953, 1359, 0.68, TRUE)       
                = 1 - 0.9569       
P(X ≥ 954) = 0.0431       
        
b) 0.0431 < 0.05       
that is the probability is less than 5% which is an 'unusual' probability       
Hence, the result in part (a) suggests,       
D. Some people are being less than honest because P(x≥954​) is less than​ 5%.