For one statistics course, among the students who purchase textbook, 70% choose physical textbook, 30% choose electronic textbook. Assume three students who made the purchases are randomly selected. Let random variable X be the number of students chosen physical textbook minus the number of students chosen electronic textbook.

1. find the probability distribution of X.

2. calculate P(X=0) and P(X=3).

3. Find the mean of X

At a local high school 80% of students who enter as freshmen go on to graduate. 20 freshmen are randomly selected.

a.

What is the probability that at most 12 students will go on to graduate? Round your answer to 4 decimal places.

b.

What is the probability that at at least 15 students will go on to graduate? Round your answer to 4 decimal places.

c.

What is the probability that at least 12 and no more than 16 students will go on to graduate? Round your answer to 4 decimal places.

What does it mean to say that we are going to use a sample to draw an inference about a population? Why is a random sample so important for this process? If we wanted a random sample of students in the cafeteria, why couldn’t we just choose the students who order Diet Pepsi with their lunch? Comment on the statement, “A random sample is like a miniature population, whereas samples that are not random are likely to be biased.” Why would the students who order Diet Pepsi with lunch not be a random sample of students in the cafeteria?

"You ask students to identify European countries on a map. On average students will identify 10% of the countries correctly. A similar test for US states indicates a 45% success rate. Asking students to identify 7 European countries and 3 US states, what is the chance that students will correctly identify at least 50% of the countries/states?"

"You have a set of 100 batteries. 13 of these batteries are defective. Testing 25 batteries, what is the probability to find 3 or more of the 25 batteries failing?"

This is observation from previous years about the impact of students working while they are enrolled in classes, due to students too much work, they are spending less time on their classes. First, the observer need to find out, on average, how many hours a week students are working. They know from previous studies that the standard deviation of this variable is about 5 hours. A survey of 200 students provides a sample mean of 7.10 hours worked. What is a 95% confidence interval based on this sample?

((NO HANDWRITING PLEASE))

Suppose that there are two schools in a region. 7% of students will move from school A to school B at the end of each year, while 11% of students will move from school B to school A. Suppose that initially 30% of students attend school A and 70% attend school B.

a) Determine the transition matrix and the initial probability vector which can be used to represent this information.

b) Find the percentage of students attending each school at the end of 3 years ( give answers to four decimal places)

The College Board wanted to test whether students graduating from private colleges and students graduating from public universities had different amounts of student loan debt. A sample of students from 146 private colleges across the country yielded an average loan debt of $29,972 with a standard deviation of $3,200. A sample of students from 225 public universities yielded an average loan debt of $28,762 with a standard deviation of $5,600. Conduct the test at the α=0.02α=0.02 level of significance.

You are a member of a training team who is preparing a training module for new nontraditional students, or students who fall outside the 18-22 age range. Rather than going immediately into college from high school, many nontraditional students enter the workforce instead. Using the andragogical assumptions in addition to the andragogical principles and training applications reviewed in chapter 2, show how your team would develop a module that trains nontraditional students in how to study and manage time.

1. In our sample of 42 students, we are interested in whether the amount of money students think a first date should cost is different based on whether they are in a romantic relationship or not. The mean amount stated by the 21 students in a relationship was $58.81, with a standard deviation of $47.17, while the 21 students not in a relationship thought first dates should cost a mean of $48.10 with a standard deviation of $24.16. State the null and alternative hypotheses, conduct the appropriate type of t test, and write a conclusion interpreting your findings.

An educator wants to study the use of clickers in the classroom. For which of the following scenarios would a two-sample t-test be appropriate?