It is known that 40% of voters in a certain electorate are in favour of a particular candidate. If a sample of size 30 is taken, what is the probability that less than 35% are in favour of this political candidate?
A)40%
B)Less than 0.10%
C)28.77%
D)None of these choices are correct.

Question

Quizplus · Accepted Answer

This is a binomial probability problem that can be approximated using the normal distribution because the sample size is large enough. The mean of the distribution ($\mu$) is $np = 30 \times 0.4 = 12$ and the standard deviation ($\sigma$) is $\sqrt{np(1-p)} = \sqrt{30 \times 0.4 \times 0.6} \approx 2.683$. To find the probability of less than 35% (which is 10.5 out of 30), we convert this to a z-score and look up the probability in a standard normal distribution table or use a calculator. The calculation of the z-score is $\frac{10.5 - 12}{2.683}$, which gives a value that corresponds to a probability of approximately 28.77%. This is a simplified explanation; the exact calculation involves more detailed steps with the normal distribution.

It Is Known That 40% of Voters in a Certain