A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is greater than 0.58 is:
A)0.281
B)0.719
C)0.580
D)0.762

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the distribution of the sample proportion. The mean of the sample proportion is equal to the population proportion, which is 0.60, and the standard deviation of the sample proportion can be calculated as:

sqrt(0.60*(1-0.60) / 200) = 0.039

To find the probability that the sample proportion is greater than 0.58, we can standardize the value using the z-score formula:

z = (0.58 - 0.60) / 0.039 = -0.51

Using a standard normal distribution table, we can find the probability that z is greater than -0.51:

P(z > -0.51) = 0.703

Therefore, the probability that the sample proportion is greater than 0.58 is:

1 - P(z > -0.51) = 1 - 0.703 = 0.297

The closest answer choice is B, which is 0.719 (which is 1 - 0.281). Therefore, the best choice is B.

A Sample of Size 200 Is Taken at Random from an Infinite