1:North Carolina State University posts the grade distributions for its courses online. Students in Statistics 101 in the Fall 2007 semester received 26% A's, 42% B's, 20% C's, 10% D's, and 2% F's. Choose a Statistics 101 student at random. To "choose at random" means to give every student the same chance to be chosen. The student's grade on a fourpoint scale (with A = 4) is a discrete random variable X with this probability distribution: Value of X 0 1 2 3 4 Probabilit 0.02 0.10 0.20 0.42 0.26 y (a) What values of random variable X are represented by the event "the student got a grade poorer than B"? Write your answer as a commaseparated list. (b) What is the probability of the event from part (a)? Q2: Canada's national statistics agency, Statistics Canada, says that the land area of Canada is 9,094,000 square kilometers. Of this land, 4,176,000 square kilometers are forested. Choose a square kilometer of land in Canada at random. (a) What is the probability that the area you choose is forested? (b) What is the probability that it is not forested? Q3:Choose a new car or light truck at random and note its color. Here are the probabilities of the most popular colors for vehicles made in North America in 2007. Color White Silver Black Red Gray Blue Probabilit 0.19 0.18 0.16 0.13 0.12 0.12 y (a) What is the probability that the vehicle you choose has any color other than the six listed? (b) What is the probability that a randomly chosen vehicle is neither Red nor White? Q4:Canada has two official languages, English and French. Choose a Canadian at random and ask, "What is your mother tongue?" Here is the distribution of responses, combining many separate languages from the broad Asia/Pacific region: Language English French Asian/Pacific Other Probabilit 0.63 0.22 0.06 ? y (a) What probability should replace "?" in the distribution? (b) What is the probability that a Canadian's mother tongue is not English? (c) What is the probability that a Canadian's mother tongue is a language other than English or French? Q5: Let X be random number between 0 and 1 produced by the idealized uniform random number generator. Use the density curve for X, shown below, to find the probabilities: a: P(X>0.6)=? b: P(X=0.13)=? Q6: A study of 12,000 ablebodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11 minutes and standard deviation 0.74 minute. Choose a student at random from this group and call his time for the mile Y. (a) Write the event "the student could run a mile in more than 8.16 minutes" in terms of the value of the random variable Y. Use the symbols "<" or ">" as appropriate to indicate the bounds on Y. (b) What is the probability of the event from part (a)? \f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f