A random sample of size 100 is taken from a population described by the proportion . Refer to Exhibit 7-6.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  . Refer to Exhibit 7-6.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 need to use the Central Limit Theorem (CLT) to approximate the sampling distribution of the sample proportion.

The mean of the sampling distribution of the sample proportion is equal to the population proportion:

μp = P = 0.11

The standard deviation of the sampling distribution of the sample proportion is given by:

σp = sqrt[(P * (1 - P)) / n]

where n is the sample size.

σp = sqrt[(0.11 * 0.89) / 100] ≈ 0.0335

To find the probability that the sample proportion is greater than 0.62, we standardize the sample proportion:

z = (0.62 - P) / σp

z = (0.62 - 0.11) / 0.0335 ≈ 13.49

Using a standard normal table or calculator, we find that the probability of a standard normal random variable being greater than 13.49 is essentially 0. Therefore,

P(sample proportion > 0.62) ≈ 0.

A Random Sample of Size 100 Is Taken from a Population