1. For a population with a Right skewed distribution, generate a sample distribution of (n = 5) and hit the 1-time button. You will see 5 random data points chosen and the mean and standard deviation of that sample are shown. Keep hitting the 1-time button many times and look at the shape of the distribution that falls out. Now hit the 5 times button to do 5 samples at a time. What distribution do you notice taking shape? Hit the 1000 times button and see what happens. How does it compare to the original right-skewed distribution? How does it compare to the original mean and standard deviation of the population? 1 b). 1bHit Reset and repeat for a population with a Uniform distribution, generate a sample distribution of (n = 5), and hit the 1-time button. You will see 5 random data points chosen and the mean and standard deviation of that sample are shown. Keep hitting the 1-time button many times and look at the shape of the distribution that falls out. Now hit the 5 times button to do 5 samples at a time. What distribution do you notice taking shape? Hit the 1000 times button and see what happens. How does it compare to the original uniform distribution? How does it compare to the original mean and standard deviation of the population? 1 c). Hit Reset and repeat for a population with a Custom distribution. Try to draw a distribution that is not even close to being Normal. Generate a sample distribution of (n = 5) and hit the 1-time button. You will see 5 random data points chosen and the mean and standard deviation of that sample are shown. Keep hitting the 1-time button many times and look at the shape of the distribution that falls out. Now hit the 5 times button to do 5 samples at a time. What distribution do you notice taking shape? Hit the 1000 times button and see what happens. How does it compare to the original distribution? How does it compare to the original mean and standard deviation of the population? 1 d). For your custom distribution, share the population mean and standard deviation as well as the mean and standard deviation of the 1000 sample means. How does the value calculate using the formula compared to the standard deviation of the 1000 sample means? 1 e). What if we did repeated samples of size n=30? What would have been the standard deviation of the sample means for your custom distribution? 6. Explain the Central Limit Theorem within the context of what you did for this discussion.