Welcome to the Lab for Module 6. In this lab we'll be getting more experience calculating probabilities for both Normal- and t- distributed random variables. Some of the functions you may need are: pnorm (x, mean = mu, sd = sigma, lower.tail = TRUE) This is the function to calculate the area under a normal curve where X~ N(u, o). Recall that "areas" of probability distributions correspond to probabilities. Therefore, if you specify lower. tail=TRUE, you are finding the P(X < x). If you specify lower.tail=FALSE, you are finding the P(X > x). pt (x, df n-1, lower.tail = TRUE) This is the function to calculate the area under a t curve where X~ taf=(n-1). For this lab we will again be using the tidyverse package. Use library (tidyverse) to load this packages. If you receive an error, you may need to reinstall the package from the bottom right pane of the R. Studio window (Packages -> Install -> "tidyverse") 1. In the Netherlands, healthy men between the ages of 65 and 79 have a distribution of serum uric acid levels that is approximately normal with mean m = 341 mol/l and standard deviation s = 79 mol/l. A. What proportion of the men have a serum uric acid level between 300 and 400 mol/1? B. What proportion of samples of size 5 have a mean serum uric acid level between 300 and 400 mol/1? C. What proportion of samples of size 10 have a mean serum uric acid level between 300 and 400 mol/1? D. Construct an interval that encloses 95 % of the means of samples of size 10.