A box haves 1,000 tiles, each with (integer) number between 1 and 10 printed on it, with 100 tiles printed with each number (i.e. there are 100 ‘1' tiles, 100 ‘2' tiles etc.). Tiles are drawn randomly from box, as well as replaced after each draw.
(a) Write down the general formula for discrete uniform probability distribution function. Now write down the probability distribution function for the random drawing of tile numbers. Is this a discrete uniform distribution?
(b) What are the mean and standard deviation of randomly drawn tile numbers?
(c) Say that you are asked to construct the sampling distribution of the mean tile number. Give a step-by-step explanation of how you would do this; you can assume a sample size of 30.
(d) Sketch (roughly) the sampling distribution of the mean tile number. Explain why the sampling distribution has this shape.
(e) What are the mean and standard error of your sampling distribution?
(f) [For bonus marks] What is the probability of drawing 30 tiles and obtaining a mean tile number of less than 4?