(a) In a 3-children family, what are the possible outcomes of gender of the children? Draw a tree diagram to list all the possible outcomes A tree diagram: (b) A survey on the nationality of the students in St. Thomas International School is conducted and the results are shown below: Students distribution in the St. Thomas School 230 250 200 150 110 85 100 25 50 Asian Eur ope an American African Nationality If TWO students are randomly selected, what is the probability that (i) both of them are European (correct to 4 decimal places); If ONE student is randomly selected, what is the probability that the (ii) student is NOT Asian (correct to 4 decimal places). Number of students

Consider the experiment of tossing a coin twice and then rolling a dice a. Develop a tree diagram for the experiment b. List the experimental outcomes c. What is the probability for each experimental outcome?  d. Is this an question based on independent event or this is mutually exclusive? Please explain your answer.

A group of students at a local university were asked about their status (undergraduate, graduate, or non-degree seeking) and how they get to campus (walk/bike or car/bus/etc.). The results are summarized in the table below. How do you get to Campus? Walk/Bike Car/Bus/etc. Total Undergraduate 80 20 100 Graduate 40 10 50 Non-degree Seeking 10 40 50 Total 130 70 200 Suppose we choose a person at random from this sample. Which of the following statements is true? (A) If the person uses a car/bus/etc. to get to campus, then he or she is more likely to be a non- degree seeking student than a degree seeking student (undergraduate or graduate). (B) If the person is an undergraduate, then he or she is more likely to use a car/bus/etc. to get to campus than to walk/bike to campus. (C) The person is more likely be a graduate student if he or she uses a car/bus/etc. to get to campus than if he or she walks/bikes to campus. (D) The person is more likely to use a car/bus/etc. to get to campus than…

A group of 11 students was selected at random and asked for their high school GPA and their freshmen GPA in college the subsequent year. The results were: Student High School GPA Freshmen GPA 1 2.0 1.6 2 2.2 2.0 3 2.6 1.8 4 2.7 2.8 5 2.8 2.1 6 3.1 2.0 7 2.9 2.6 8 3.2 2.2 9 3.3 2.6 10 3.6 3.0 We would like to know whether there is a linear relationship between the high school GPA and the college freshmen GPA, and we would like to be able to predict the freshmen GPA, if we know that the high school GPA of another student is, say, 3.4.  Provide the two requested scatter plots for this data (put college freshman GPA on the Y (vertical) axis!).  a) What would be your approximate 95% prediction interval for question (g)? b) Show your scatterplot with the predicted trend line below