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 less than 0.58 is
A)0.281
B)0.719
C)0.580
D)0.762

Question

Quizplus · Accepted Answer

The sample proportion follows the normal distribution with mean equal to population proportion i.e 0.60 and standard deviation equal to sqrt((0.60*0.40)/200) = 0.0499 (using formula for standard deviation of sample proportion).
Now, we need to calculate the z-score for sample proportion less than 0.58:
z = (0.58 - 0.60) / 0.0499 = -0.401
Using standard normal distribution table, the area/probability to the left of z=-0.401 is 0.281 (approximately).
Therefore, the probability that the sample proportion is less than 0.58 is 0.281.

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