To apply the Central Limit Theorem on sample proportions in a One Sample Proportion test, the sample size and the population proportion under the null hypothesis need to satisfy certain conditions. Which of the following scenarios meet the requirement? A. The sample size is 50 and the population proportion under null hypothesis is 25%.B. The sample size is 70 and the population proportion under null hypothesis is 90%.C. The sample size is 50 and the population proportion under null hypothesis is 15%.D. The sample size is 200 and the population proportion under null hypothesis is 4%.

the correct answer is $7.38

step-by-step explanation:

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.