A random sample of size 100 is taken from a population described by the proportion p = 0.60.The probability that the sample proportion is greater than 0.62 is _______.
A) 0.3409
B) 0.4082
C) 0.6591

Question

A random sample of size 100 is taken from a population described by the proportion p = 0.60.The probability that the sample proportion is greater than 0.62 is _______.
A) 0.3409 
B) 0.4082 
C) 0.6591

Quizplus · Accepted Answer

We can use the central limit theorem (CLT) to approximate the distribution of the sample proportion. The mean of the sample proportion is equal to the population proportion p, and the standard deviation of the sample proportion is:

standard deviation = sqrt((p(1-p))/n)

where n is the sample size.

So, in this case, the standard deviation is:

standard deviation = sqrt((0.60(1-0.60))/100) = 0.0471

To calculate the probability that the sample proportion is greater than 0.62, we can standardize the sample proportion using the formula:

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

So, for a sample proportion of 0.62:

z = (0.62 - 0.60) / 0.0471 = 0.4255

We can then use a standard normal distribution table to find the probability that z is greater than 0.4255. This probability is approximately 0.3409.

Therefore, the probability that the sample proportion is greater than 0.62 is 0.3409.

A Random Sample of Size 100 Is Taken from a Population