Question

The proportion of adult women in a certain geographical region is approximately 51%. A marketing survey telephones 400 people at random. Complete parts a through e below.

a) What is the sampling distribution of the observed proportion that are women?
A. Approximately Uniform
B. Approximately Normal
C. Approximately Exponential
D. None of these

Answer 1

The sampling distribution of the observed proportion of women is Approximately Normal due to the large sample size and the conditions of the Central Limit Theorem being met. The correct option is option B.

Step-by-step explanation:

The sampling distribution of the observed proportion of women in a survey where a marketing company telephones 400 people at random is Question A in the student's homework. Since the sample size is large (n=400) and the population proportion is known to be approximately 51%, we can use the Central Limit Theorem to determine the shape of the sampling distribution. The Central Limit Theorem tells us that for large sample sizes, the sampling distribution of the sample proportion will be approximately normal, given that the following conditions are met: np and n(1-p) are both greater than 5. In our case, with n=400 and p=0.51, both np=400(0.51)=204 and n(1-p)=400(0.49)=196 are greater than 5.

Therefore, the answer to Question A is B. Approximately Normal.