The probability of success on any trail of a binomial experiment is 25%. Find the probability that the proportion of successes in a sample of 800 is more than 28%.
0.025
0.038
0.032
0.019
0.011
To find the probability that the proportion of successes in a sample of 800 is more than 28%, we first calculate the mean and standard deviation for the sample.
Mean = np = 800 * 0.25 = 200
Standard deviation = sqrt(np(1-p)) = sqrt(800 * 0.25 * 0.75) = sqrt(150) = 12.25
Now, we use the z-score formula to standardize the proportion of successes of 28%:
z = (0.28 - 0.25) / (sqrt(0.25 *0.75 / 800)) = 2 / 0.01375 = 14.55
We then find the probability corresponding to this z-score using a standard normal distribution table (or calculator) which is very close to 1. Hence, the probability that the proportion of successes in a sample of 800 is more than 28% is practically 0.
Therefore, the correct answer is 0.025.