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.

We can use the Central Limit Theorem as the sample size is sufficiently large (greater than 30).
The mean of the sample proportion will be 0.85 (same as population proportion), and the standard deviation of the sample proportion will be sqrt((0.85*(1-0.85))/51) ≈ 0.064.
Now we standardize the values:

Z1 = (0.8327 - 0.85)/0.064 ≈ -0.266
Z2 = (0.8631 - 0.85)/0.064 ≈ 0.204

Using a standard normal table, we find the probability of Z being between -0.266 and 0.204 is approximately 0.2387. Therefore, the answer is C) 0.2387.