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 between 0.58 and 0.62 is:
A)0.4380
B)0.0320
C)0.0200
D)None of these choices.

Question

Quizplus · Accepted Answer

First, we need to find the standard error of the sample proportion:
SE = sqrt(p(1-p)/n) = sqrt(0.6(1-0.6)/200) = 0.0387

Next, we need to standardize the sample proportion using the equation:
z = (p̂ - p) / SE

We want to find the probability that the sample proportion (p̂) is between 0.58 and 0.62, which can be rewritten as the probability that the standardized z-score is between:

z1 = (0.58 - 0.6) / 0.0387 = -0.515
z2 = (0.62 - 0.6) / 0.0387 = 0.515

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:
P(-0.515 < z < 0.515) = 0.8779 - 0.4399 = 0.4380

Therefore, the answer is choice A) 0.4380.

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