A sample of 66 observations will be taken from a process (an infinite population). The population proportion equals .12. The probability that the sample proportion will be less than .1768 is _____.
A) .0568
B) .0778
C) .4222
D) .9222

Question

Quizplus · Accepted Answer

The sample proportion follows a normal distribution with mean equal to the population proportion (0.12) and standard deviation equal to sqrt[(0.12)(0.88)/66]. To find the probability that the sample proportion is less than 0.1768, we calculate the Z-score for 0.1768 and use the standard normal distribution. The calculation shows that the probability is high, leading to the correct answer being 0.9222.

A Sample of 66 Observations Will Be Taken from a Process