2. I am intrigued by my friend observation. He was convinced that the distributions of the pours is normal with mean 5.50: and standard deviation 0.25 02. To test this I had to drink 20 shots to obtain a reasonable sized sample (all in the interest of science of course). Before I drank each of the glasses I measured the content. I am not going to write the exact numbers because I do not remember them anymore. Luckily, I wrote the summary statistics on a napkin which I found the next day in my pocket. Here they are: :E - 5.565, 359 : 1.607, 5(X; : c.1365, K(X) : 4.116. (a) I distinctly remember that the measure I used only gave me one digit. How is it possible that :1\": : 5.565 has 3 digits? (b) Perform a test statistics to see if the distribution has heavy tails. Write the hypotheses test statistics, calculate the pvalue and state your conclusion