Paper 1 · confidence intervals / Central Limit Theorem

According to the Central Limit Theorem, for a sufficiently large sample size $n$ drawn from any population with mean $\mu$ and variance $\sigma^2$ , the distribution of the sample mean $\bar{X}$ is approximately

N(\mu, \sigma^2/n)

N(\mu, \sigma^2)

N(n\mu, \sigma^2/n)

N(\mu/n, \sigma^2)

Explanation: The Central Limit Theorem states that for large

n

, the sample mean is approximately normally distributed with the same mean

\mu

as the population but with reduced variance

\sigma^2/n

, since averaging

n

observations shrinks the spread by a factor of

n

Derived from ZIMSEC Statistics Paper 1, November 2021, Q1

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