Answer to Question #279849 in Statistics and Probability for rico

Question

a die has 6 faces having dots x = 1, 2 3 4 5 6. Given the population, illustrate the central limit theorem and the sampling distrubution of sample mean n= 3. I need the answer asap. Thank you.

Answer 1

The average of three dice is taken as the sample mean of all sample and the results of 30 sample means are plotted on the frequency curve and it represents a normal distribution.

As per central limit theorem,

The sample means follow normal distribution as can be seen from the relative frequency curve.

If number of samples will be increased from 30 to larger number then the curve would perfectly fit normal distribution.