Step 2: Lets check pre-conditions to make sure our samples are valid and can be expected to be normally distributed around p. Write your preconditions below.

Sure, let's proceed with the preconditions to ensure our samples are valid and can be expected to be normally distributed around p.

1. Random Sampling: Ensure that the samples are collected randomly. This helps in avoiding any bias in the data collection process.

2. Sample Size: The sample size should be sufficiently large. According to the Central Limit Theorem, a sample size of at least 30 is generally considered adequate for the sample mean to be approximately normally distributed.

3. Independence: Each sample should be independent of the others. This means that the selection of one sample should not influence the selection of another.

4. Population Proportion (p): The population proportion (p) should be known or estimated accurately. This is crucial for comparing the sample proportion to the population proportion.

5. np and n(1-p) Conditions: Check that both np and n(1-p) are greater than 5. This ensures that the sample distribution of the proportion can be approximated by a normal distribution.

6. No Outliers: Ensure there are no significant outliers in the data, as they can skew the results and affect the normality of the distribution.

By verifying these preconditions, we can confidently proceed with the assumption that our samples are valid and normally distributed around the population proportion p.