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)0.4314
B)0.0320
C)0.0200
D)None of these choices.

Question

Quizplus · Accepted Answer

The sample proportion, denoted by p̂, follows a normal distribution with mean equal to the population proportion, denoted by p, and standard deviation equal to

√(p(1-p)/n)

Here, p=0.6 and n=200.

Thus, we have 
p̂ ~ N(0.6, √(0.6(0.4)/200))

= N(0.6, 0.039)

The probability that the sample proportion is between 0.58 and 0.62 can be written as:

P(0.58 < p̂ < 0.62)

= P[(0.58-0.6)/0.039 < (p̂-0.6)/0.039 < (0.62-0.6)/0.039)

= P(-0.51 < z < 0.51)

Using a standard normal distribution table, we can find:

P(-0.51 < z < 0.51) = 0.4314

Therefore, the probability that the sample proportion is between 0.58 and 0.62 is 0.4314, which is answer choice A.

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