Use the following information for questions:
Based on the 2000 Census, the proportion of the California population aged 15 years old or older who are married is p = 0.524. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of married persons ( $\hat{p}$) is to be calculated.
-What is the approximate probability that less than 50% of the people in the sample are married?
A) 0.0158
B) 0.0645
C) 0.5240
D) 0.9355

Question

Use the following information for questions:
 Based on the 2000 Census, the proportion of the California population aged 15 years old or older who are married is p = 0.524. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of married persons ( $\hat{p}$) is to be calculated.
-What is the approximate probability that less than 50% of the people in the sample are married?
A) 0.0158
B) 0.0645
C) 0.5240
D) 0.9355

Quizplus · Accepted Answer

The sampling distribution of the sample proportion $\hat{p}$ is approximately normal with mean $p = 0.524$ and standard deviation $\sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.524 \times 0.476}{1000}}$. Using the standard normal distribution, the probability that $\hat{p} < 0.5$ can be calculated, which is approximately 0.0645.

Use the Following Information for Questions: Based on the 2000

Use the Following Information for Questions:
Based on the 2000