A population proportion is 0.40. A random sample of size 200 will be taken and the sample proportion p will be used to estimate the population proportion. Use the z-table. Round your answers to four decimal places. a. What is the probability that the sample proportion will be within ±0.03 of the population proportion? b. What is the probability that the sample proportion will be within ±0.05 of the population proportion?

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**Problem Statement: Estimating Population Proportion**

A population proportion is given as **0.40**. A random sample of size **200** will be taken, and the sample proportion (\(\tilde{p}\)) will be used to estimate the population proportion. To find probabilities, use the **z-table**. Ensure your answers are rounded to four decimal places.

**Questions:**

**a.** What is the probability that the sample proportion will be within \(\pm 0.03\) of the population proportion?
- [Input Box for Answer]

**b.** What is the probability that the sample proportion will be within \(\pm 0.05\) of the population proportion?
- [Input Box for Answer]
Transcribed Image Text:**Problem Statement: Estimating Population Proportion** A population proportion is given as **0.40**. A random sample of size **200** will be taken, and the sample proportion (\(\tilde{p}\)) will be used to estimate the population proportion. To find probabilities, use the **z-table**. Ensure your answers are rounded to four decimal places. **Questions:** **a.** What is the probability that the sample proportion will be within \(\pm 0.03\) of the population proportion? - [Input Box for Answer] **b.** What is the probability that the sample proportion will be within \(\pm 0.05\) of the population proportion? - [Input Box for Answer]
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