Which of the following is not correct about the Central Limit Theorem?

The correct answer is Option (4) → The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger.

The Central Limit Theorem says that, for a large sample, the sampling distribution of the sample mean is approximately normal, whatever the shape of the population.

Options (1), (2) and (3) are true. The normal curve is the bell-shaped curve; a sample of 30 or more is the usual rule for “large”; and the standard error \(\frac{\sigma}{\sqrt{n}}\) falls as n grows, so estimates of the population become more accurate.

Option (4) is not correct: the sampling distribution approaches a normal distribution, not a Poisson distribution.

CBSE Applied Mathematics (Class XII):
Central Limit Theorem