Question

select the correct answer.

the programmer at a local public radio station is compiling data on listeners who stream podcasts. an executive for the national broadcaster has communicated that the overall population mean is 20,500 with a standard deviation of 2,180. the local programmer has a sample of 30 podcasts for her station. by the central limit theorem, which interval do about 99.7% of the sample means fall within?

19,306 and 21,694
20,282 and 20,718
20,102 and 20,898
19,704 and 21,296

Explanation:

Calculate the standard error of the mean

$$ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{2180}{\sqrt{30}} \approx \frac{2180}{5.4772} \approx 398.01 $$

Apply the empirical rule for 99.7% confidence

$$
LATEXBLOCK0
$$

Identify the matching interval

$$ [19306, 21694] $$

Answer:

• (A) 19,306 and 21,694 (Correct answer)
• (B) 20,282 and 20,718
• (C) 20,102 and 20,898
• (D) 19,704 and 21,296