Question

If the distribution of the population has a nonzero standard deviation and mean 10 then the probability that an individual data value will be greater than 11 is always less than the probability that the mean of 25 randomly selected data values will be greater than 11

TRUE OR FALSE?

Answer 1

FALSE

Explanation:

The central limit theorem tell us that for a random sample of size n, the average of the sample will be approximately normally distributed with mean
`\mu` and variance
`\sigma^2/n`, where
`\mu` and
`\sigma^2` are the mean a variance respectively of the sampling distribution. This always that the mean and the variance are both finite and the sample size n is greater than 30. We could use the central limit theorem, but in this case does not help us because we are considering 25 randomly selected data values, besides, we do not know the distribution of the original population.