Question

1. What is the Central Limit Theorem? Try to state it in your own words.

States that the sample means of large sized samples will be normally distrution

2. Consider the random variable x, where x is the number of dots after rolling a die. Make a sketch of the probability distribution of this variable. What is the expected value of x?

3. Now consider the random variable that is the average number of dots after four rolls. Is this variable normally distributed? Explain.

Answer 1

Central limit theorem states that whatever be the distribution of parent population, when the sample size is large , the sample mean of the distribution follows Normal distribution with mean and variance .

When rolling die , the possible outcomes of the experiment are 1, 2,3, 4,5,6 with probability 1/6 each.

Expected value ==

=

=

Average number of dots after four roll is not a normal distribution because sample size is small(4). Central limit theorem can applied only for large sample sizes.