A sample of 400 observations will be taken from a process (an infinite population). The population proportion equals .8. The probability that the sample proportion will be greater than 0.83 is _____.
A) .4332
B) .9332
C) .0668
D) .5668

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the distribution of sample proportions. The mean of the sample proportions will be equal to the population proportion, which is 0.8 in this case. The standard deviation of the sample proportions can be calculated using the formula:

standard deviation = sqrt[p*(1-p)/n]

where p is the population proportion and n is the sample size. Plugging in the values, we get:

standard deviation = sqrt[0.8*(1-0.8)/400] = 0.0224

We can standardize the sample proportion using the formula:

z = (sample proportion - population proportion) / standard deviation

Plugging in the values, we get:

z = (0.83 - 0.8) / 0.0224 = 1.4732

We can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is greater than 1.4732. The answer is approximately 0.0668. Therefore, the probability that the sample proportion will be greater than 0.83 is 0.0668. Answer choice C is correct.

A Sample of 400 Observations Will Be Taken from a Process