(a) Does the distribution of sample means appear normal (i.e. like a normal distribution)? Explain.

Question

Exercise #1: Using the Normal Distribution simulator, run a simulation for a population with a mean of  = 50
and a standard deviation of  =15 for a sample size of 30. Run 100 simulations.

Answer 1

There is a simulator on this website https://www.mathsisfun.com/data/normal-distribution-simulator.html

With it you can generate a sample dataset, using the figures in your question. The simulator does all calculations for you. Positive skew means the data is bunched to the left, negative skew it’s bunched to the right. Watch out for whether the mean is greater or less than the peak (where there is most of the data). Greater (to the right) means positive skew, and less than (to the left) means negative skew. If you suspect skew, sketch the data on graph paper and see where the data is more bunched. A normal distribution is bell-shaped with “tails” roughly the same shape and spread.