Statistics exam 2

Total area under the standard normal distribution curve

1 (or 100%) — because the normal distribution represents the entire probability space.

Sampling error

The difference between the sample means and the population mean due to random sampling variability.

Central limit theorem

It says that, regardless of the population's distribution, the distribution of sample means approaches a normal distribution as the sample size increases (typically n≥30).

Conditions for normal approximation to binomial distribution

The approximation is valid if both: n⋅p≥5 and n⋅q≥5 (where q=1−p).

Margin of error

The maximum likely difference between the sample statistic and the population parameter, reflecting the uncertainty in the estimate.

Define the central limit theorem

When you take a large enough sample from any population, the distribution of the sample means will be approximately normal (bell-shaped), even if the original population is not normally distributed.