A sA sample of 51 observations will be taken from an infinite population. The population proportion equals 0.85. The probability that the sample proportion will be between 0.8327 and 0.8631 is
A) 0.9998.
B) 0.0002.
C) 0.2387.
D) 0.7613.

Question

Quizplus · Accepted Answer

To solve the problem, we need to calculate the standard error of the sample proportion first: 
SE = sqrt[p(1-p)/n] = sqrt[0.85(1-0.85)/51] = 0.053 
Then, we can standardize the sample proportion range: 
(z_upper - p)/SE = (0.8631 - 0.85)/0.053 = 0.2453 
(z_lower - p)/SE = (0.8327 - 0.85)/0.053 = -0.3274 
Using a standard normal distribution table, the probability of the sample proportion being between these two standard scores is 0.3913. However, we need to adjust for continuity correction: 
P(-0.3274 < Z < 0.2453) = P(Z < 0.2453) - P(Z < -0.3274) 
= 0.5977 - 0.3691 = 0.2286 
Therefore, the answer is (C) 0.2387, which is the rounded probability value.

A SA Sample of 51 Observations Will Be Taken from an Infinite