Part 1:Probability Review

1. Suppose that a popular grocery store tells customers the probability they will have to wait in line for at least 3 minutes is 0.25. What does the grocery store mean by "at least"?

2. Return to Question 1.If the grocery store tells customers the probability they will have to wait in line for at most 5 minutes is 0.65, what is meant by "at most"?

Did you know that the first digits of numbers in financial records often follow something known as Benford's Law? If you look at a company's financial records and choose one record at random, Benford's Law gives the following probability model for the first digit of that record (and note that the first digit cannot be zero). This is important to understand because faked numbers in invoices, expense account claims, or tax returns often display patterns that aren't present in real records. Please use this information to answer Questions 3 and 4.

First digit	1	2	3	4	5	6	7	8	9
Probability	0.301	0.176	0.125	0.097	0.079	0.067	0.058	0.051	0.046

3. What is the probability that the first digit of a real financial record is an even number?

4. What is the probability that the first digit of a real financial record is not 2?

5. The following probability model was constructed based on the final grades awarded to students in a large biology course. One probability is left out of this modelthe probability of receiving a C. Explain what that probability must be and how you know.

Grade	A	B	C	D	E
Probability	0.22	0.31	?	0.15	0.03

6. At a large university, the probability that a randomly chosen student lives on campus is 0.32. This means that _________% of the students at this university must live on campus.

7. What is wrong with the following statement?

On the OSU campus, the probability is 1.15 that the color of a randomly selected vehicle from the Tuttle Parking Garage is red.

Part 2: Sampling Distributions

In Chapter 18, you are introduced to the idea of asampling distribution. The purpose of the next few questions is to help you better understand what a sampling distribution is and how we can use what is known about sampling distributions to answer different kinds of questions.

Have you ever wondered what percentage of college students change their major? It turns out that in the population of all college students, 75% change their major.

8. Suppose you survey a random sample ofn= 40 college students and 26 of these students report having changed their major. What will your sample proportion, or , be? Please calculate this number below.

9. The number you wrote in response to Question 8 describes a sample. As you learned earlier in the semester, we call a number that describes a sample a _________________________.

10. As previously mentioned, in the population of all college students, 75% have changed their major. Written as a proportion, this number would be 0.75, and we use the symbolpto denote a population proportion. We would consider the population proportion to be a_____________________ because it's a number that describes a population.

Imagine now that 30 of your STAT 1350 classmates each survey a random sample ofn= 40 college students. Each classmate then determines the proportion of the students in the sample who report having changed their major. The graph belowcalled a dot plotshows each of these sample proportions.Each proportion appears as a dot above a number line, and the number line gives us different values of our sample proportions. If any dots are stacked in a column, it would mean that more than one sample resulted in that sample proportion. For example, there are four dots stacked in a column at 0.78, and this means that four sample proportions were 0.78.