Question

Cleary and correctly explain the central limit theorem(definition and how it works) and why is it useful in statistics.

Answer 1

Sol:

Definition:

sampling distribution of sample means will become normal as the sample size increases.

For large sample which is n>30

Even though we do not know the population distribution irrespective of that sample follows normal distribution.

sample mean=xbar=mu

and sample stddev=

Applications:

1)its critical to inferential statistics.

2)In estimation, we can now determine a margin of error and a confidence interval.

3)In hypothesis testing,we can make decisions with a known probability of making statistical error.

4)used in pprobability theory.