Question

If p=0.5 and the distribution is normal what is the sample size?

This portability distribution p is called [blank] distribution

Answer 1

In your question, when you refer to \( p = 0.5 \) and mention a normal distribution, it seems that you are discussing the sample size for a proportion in a statistics context. The proportion \( p \) typically refers to the probability of success in a binomial distribution.

When calculating the sample size for proportions, the formula used is derived from the normal approximation to the binomial distribution when \( n \) is sufficiently large.

The formula to calculate the sample size \( n \) for estimating a proportion is:

\[
n = \left( \frac{Z^2 \cdot p \cdot (1 - p)}{E^2} \right)
\]

Where:
- \( Z \) is the Z-score corresponding to the desired confidence level.
- \( p \) is the estimated proportion (in this case, 0.5).
- \( E \) is the margin of error you are willing to accept.

### To complete your statement:

Since you mentioned \( p = 0.5 \), you can say that the distribution you are dealing with is called the **binomial distribution**.

In the context of proportions, it is understood that for large sample sizes, the binomial distribution can be approximated by a normal distribution, which is why you might see "normal distribution" mentioned in connection with \( p \). However, the underlying discrete distribution is indeed the binomial distribution.

If you provide a desired confidence level and margin of error, I can help you calculate the sample size using the formula mentioned above.