To find the 95% confidence interval for a sample, we typically use the normal distribution when the sample size is large (usually n > 30) or when the population standard deviation is known. For smaller sample sizes, the t-distribution is often used, especially if the underlying population is assumed to be normally distributed.
In your case, you provided the lower and upper bounds of the confidence interval:
- Lower bound: 0.156
- Upper bound: 0.324
If you're looking for specific rounding to the nearest thousandths, the bounds you've provided are already in that format, as both numbers have three digits after the decimal point.
Thus, the confidence interval can be explicitly stated as:
\[ (0.156, 0.324) \]
Regarding the distribution used, if we assume the conditions for using the normal distribution are met (e.g., large sample size or known population standard deviation), then the normal distribution is used. If the sample size was small and the population standard deviation was not known, we would use the t-distribution.