9. (a) (2 points) Using R, create a normally distributed variable, with 500 observations, a mean of 30, and standard deviation of 10. Be sure to set the seed to 6480 before you create your variable....

9. (a) (2 points) Using R, create a normally distributed variable, with 500 observations, a mean of 30, and standard deviation of 10. Be sure to set the seed to 6480 before you create your variable. What is the mean of your variable? Does it deviate from 30? Why, or why not? (b) (2 points) Using the pnorm function in R, what is the probability of observing an data point that is 15 or less, for the following RV: X N(µ = 20, σ2 = 16)? Show the answer and the R code. (c) (2 points) Using the pnorm function in R, what is the probability of observing an data point that is greater than 3 for the following RV: X N(µ = 2, σ2 = 4)? Show the answer and the R code. (d) (3 points) Suppose you are an election monitor. You know that the probability of voting for the Democratic candidate in your district is 0.68. You observe 20 voters come into the polling station; 17 voted Democratic. Assuming that these voters’ are representative of average voter in the district and that their votes are independent from each other, what is the probability that at least 17 out of 20 voters would vote Democratic. Show the answer and the appropriate R cod