In one city, 75 percent of residents report that they regularly recycle. In a second city, 90 percent of residents report that they regularly recycle. Simple random samples of 75 residents are selected from each city. Which of the following statements is correct about the approximate normality of the sampling distribution of the difference in sample proportions of residents who report that they regularly recycle?

Question

Hillary Roberts

Advanced Placement (AP)

20 June, 18:15

In one city, 75 percent of residents report that they regularly recycle. In a second city, 90 percent of residents report that they regularly recycle. Simple random samples of 75 residents are selected from each city. Which of the following statements is correct about the approximate normality of the sampling distribution of the difference in sample proportions of residents who report that they regularly recycle?

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Answers (2)

Know the Answer?

Alfonso Foley · Answer 1

The sampling distribution is approximately normal because both sample sizes are large enough.

Explanation:

The Central Limit Theorem states that a sample of 40 or more makes for a normal distribution regardless of shape.

Annabella · Answer 2

B

Explanation:

Since this is for proportions, you should use the np greater than or equal to 10 and n (1-p) greater than or equal to 10, not the Central Limit theorem. Using math, we can deduce that 0.25 (75) is greater than 10 while 0.1 (75) is not greater than 10. Therefore, the answer is that city one's population is big enough while city two's population is too small. I got those numbers by 1-0.9 and 1-0.75 (You usually want to test the smallest values to see if they exceed 10, it's the fastest way to find holes on a problem).