R Problem: Please include all relevant R codes and outputs for full credit.

Consider the dataset Getting2NoUF2020.csv collected from the Getting to Know You Survey at the beginning of the semester. The dataset can be downloaded at http://stat.umn.edu/~wuxxx725/data/ Getting2NoUF2020.csv, and its description can be found at http://stat.umn.edu/~wuxxx725/data/ Getting2NoUF2020.pdf.

For parts (a)-(c), let X denote the number of traffic tickets that a UMN student has received.

(a) Run the following codes to load the dataset and obtain the distribution of X:

NoU <- read.csv("http://stat.umn.edu/~wuxxx725/data/Getting2NoUF2020.csv", header = T) attach(NoU) n <- sum(!is.na(traffic.tickets)) table(traffic.tickets) / n

(b) Assume that the frequency table you obtained in part (a) represents the distribution of

X for ALL the UMN students (rather than a sample from the STAT 3011 students). Use

the formula for on page 50 of the lecture notes to calculate the mean of X. Interpret.

(Note: You may round the probabilities to 3 decimal places.)

(c) Use the formula for on page 50 of the lecture notes to calculate the standard deviation of X. For parts (d)-(f), let Y denote the height of a UMN student, in inches.

(d) Use the R command hist(height, breaks = 15) to view the shape of the distribution of Y . Do you think Y is approximately normally distributed? Explain.

(e) Regardless of your answer to part (d) above, assume that Y follows a normal distribution with mean = 66.6 and standard deviation = 4.1. What is the probability that a randomly chosen student is at most 68 inches tall?

(f) Find the height y such that 85% of all UMN students are shorter than y inches tall.