Tabulation of a strike vote showed that 90% of those voting cast their ballot in favour of strike action. You take a sample of 50 voters. Assume this to be a binomial distribution. What is the probability that more than 45 of the voters from your sample voted in favour of strike action?
A) 0.50
B) 0.0948
C) 0.5948
D) 0.4052

Question

Quizplus · Accepted Answer

We can use the binomial distribution formula to solve this problem:

P(X > 45) = 1 - P(X ≤ 45)

where X is the number of voters in favor of strike action in a sample of 50 voters. Since the proportion of voters in favor of strike action is 0.9, the probability of a voter being in favor of strike action is p = 0.9 and the probability of a voter not being in favor of strike action is q = 1 - p = 0.1.

Using the binomial distribution formula, we have:

P(X ≤ 45) = Σi=0^45 (50 choose i) * 0.9^i * 0.1^(50-i)

Using a calculator, we get P(X ≤ 45) ≈ 0.5948.

Therefore,

P(X > 45) = 1 - P(X ≤ 45)
            = 1 - 0.5948
            = 0.4052

So the probability that more than 45 of the voters from the sample voted in favour of strike action is 0.4052. Therefore, the best choice is D.

Tabulation of a Strike Vote Showed That 90% of Those