the sample proportion \hat{\pi} for a random sample of 60 US adults regarding whether they have not read a book in any format in the past 12 months is approximately normally distributed with a mean of 0.23 and a standard deviation of approximately 0.0543.

The problem describes the sample proportion (\(\hat{\pi}\)) from a random sample of 60 U.S. adults regarding whether they haven't read a book in the past 12 months. The given values are:

- Mean (\(\mu_{\hat{\pi}}\)) = 0.23
- Standard deviation (\(\sigma_{\hat{\pi}}\)) = 0.0543
- Sample size \(n = 60\)

Since the sample proportion \(\hat{\pi}\) is approximately normally distributed, we can use this information to answer several questions or compute probabilities.

Would you like help with calculating probabilities, constructing confidence intervals, or testing hypotheses using this information?

Here are 5 potential questions to explore:

1. What is the probability that the sample proportion is less than 0.2?
2. What is the probability that the sample proportion is more than 0.25?
3. How do you construct a 95% confidence interval for the true population proportion?
4. How do you test if the population proportion is significantly different from 0.20?
5. What is the probability that the sample proportion falls between 0.2 and 0.25?

**Tip:** When dealing with sample proportions, it's often useful to check if the conditions for normal approximation (np and n(1-p)) are met for a more accurate approximation.

The sample proportion \hat{\pi} for a random sample of 60 US adults regarding whether they have not read a book in any format in the past 12 months is approximately normally distributed with a mean of 0.23 and a standard deviation of approximately 0.0543.

Explore the normal distribution of the sample proportion \hat{\pi} for a random sample of 60 US adults who haven't read a book in the past 12 months, with a mean of 0.23 and a standard deviation of 0.0543. Learn about calculating probabilities, constructing confidence intervals, and hypothesis testing using this statistical model. Ideal for advanced high school or undergraduate statistics students.

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