Question

According to the central limit theorem: a. The mean of a sample from a population that is not normally distributed will tend towards a normal distribution if the sample size is large b. The probability of a sample standard deviation will converge towards the population variance as the sample standard deviation increases c. The median of a sample from a population that is normally

Answer 1

a. The mean of a sample from a population that is not normally distributed will tend towards a normal distribution if the sample size is large.

Explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

So, according to the above text, the correct answer is given by option a, that is, if the sample is large, the sampling distribution of the sample mean will be approximately normal, that is, trend towards a normal distribution.