Suppose that at any sitting of ECON 201, 30% of the students are first year; 35% are second year; 20% are final year and 15% are qualifying to enter various programs (assume mutually exclusive). From records of the Statistics department, it was found that 20% of the first-year students get A; 30% of the second-year students get A; 35% of the final year students get A; 25% of the qualifying students get A. What is the probability a randomly chosen student will get an A? Given that a student got an A, what is the probability the student was first year? Second year? Third year? Qualifying?

Suppose that at any sitting of ECON 201, 30% of the students are first year; 35% are second year; 20% are final year and 15% are qualifying to enter various programs (assume mutually exclusive). From records of the Statistics department, it was found that 20% of the first-year students get A; 30% of the second-year students get A; 35% of the final year students get A; 25% of the qualifying students get A. What is the probability a randomly chosen student will get an A? Given that a student got an A, what is the probability the student was first year? Second year? Third year? Qualifying?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

4. A college wants to investigate whether students perform better on mornings that they have hada nutritious breakfast compared to mornings that they have not.You randomly recruit 100 students and tell each of them to come to the lab in two different mornings:each morning they will be offered some breakfast and will take a test. Each student will receivethe light breakfast one time and the nutritious breakfast the other time (some will receive the lightbreakfast first, the others will receive the nutritious breakfast first, and the second time they switch). The average difference in a student’s score after eating the nutritious breakfast and their score aftereating a light breakfast is 4.5, and the standard deviation of this difference is 3.6. Thus we aredoing students nutritious breakfast scores minus the light breakfast scores. a. Construct a 95% confidence interval for the difference in the average score of students afterhaving a nutritious breakfast and the average score of…
6) A small business owner you follow on TikTok is SO EXCITED because last month, she was able to begin selling her product in a popular chain store around the nation. Her contract with the chain store says that at any time, there will be at least 20 of her products sitting out on the shelves. She wants to conduct a survey to see if that is true. She visits 5 of the local chain stores around her and records the number of products of hers that are on the shelves. She will then construct a 95% confidence interval to determine the mean number of products on the shelves for all of the stores. (a) Discuss whether this study meets the each of the conditions for constructing a confidence interval. If one of the conditions has not been met, what additional information would be required or what change in the study would you recommend? (b) If, instead of constructing a 95% confidence interval, the business owner constructed a 98% confidence interval, would the 98% interval be wider, narrower, or…
9. A group of 50 single men were asked which dating apps they had on their phones. The follo data were collected: 33 of the men had the Tinder app. 30 of the men had the Coffee Meets Bagel app. 26 of the men had the Hinge app. 16 of the men had both the Tinder and Coffee Meets Bagel apps. 14 of the men had both Tinder and Hinge apps. 18 men had both Hinge and Coffee Meets Bagel apps. 7 men had all three apps on their phones. a) Represent this information in a Venn diagram: b) Calculate the number of single men who have none of these apps on their phone. c) How many single men only had Tinder on their phone? d) How many students own at most two of the apps?
2. A new pill is touted to improve the memory retention capability of teenagers aging 13 to 16 years old. To test this claim, twenty teenagers of the same age range are randomly picked to read the first two chapters of the book "Harry Potter and the Philosopher's Stone" after which they are asked to enumerate the number of verbs they remember from those chapters. Then they are given the new pill to be taken once daily for 7 days. At the end of 7 days, they are asked to read the same two chapters and enumerate the number of verbs they remember. The results are tabulated below: Number of verbs remembered Number of verbs remembered Тeen before taking the pill (X1) after taking the pill (X2) 1 6. 7 10 3 14 15 4 7 9. 8 12 4 10 7 5 7 8 3 9. 9 9 10 10 10 12 11 6. 12 8 9 13 4 10 14 8 8 15 9 13 16 6. 9. 17 11 13 18 7 6 19 20 8 At the 1% level of significance, what can you conclude? Assume normality of the differences.
he National Football League (NFL) holds its annual draft of the nation's best college football players in April each year. Prior to the draft, various sporting news services project the players who will be drafted along with the order in which each will be selected in what are called mock drafts. Players who are considered to have superior potential as professional football players are selected earlier in the draft. Suppose the following table shows projections by one mock draft service of what position in the first round players from the Atlantic Coast Conference, the Big Ten Conference, the PAC-12 Conference, and the Southeastern Conference will be selected. ACC Big Ten PAC-12 SEC CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition Florida State 4 Iowa 9 USC 1 Florida 2 Clemson 5 Michigan St 10 Oregon 6 Alabama 3 Miami 7 Nebraska 14 Oregon 15 Kentucky 8 Georgia Tech 13…
7.) Several years ago, the US began running out of telephone numbers. Telephone companies introduced new area codes and numbers were used up, and eventually almost all area codes were used up. (a) Until recently, all area codes had a 0 or 1 as the middle digit, and the first digit could not be 0 or 1. How many such area codes are possible? (b) The actual number of area codes under this system was 152. What could be the cause of the discrepancy between this number and your answer to part (a)?
5. A psychologist at a private psychiatric hospital was asked to determine whether there was any clear difference in the length of stay of patients with different categories of diagnosis. Looking at the last four patients in each of the three major categories, the results (in terms of weeks of stay) were as follows: Diagnosis Category Cognitive Disorders 12, Affective Disorders Drug-Related Conditions 7. 8. 6. 8. 10 5. 6. 12 11 10 Mı=6 M2 = 10 M3 = 10 %3D %3D SS, = 2 SS2 = 10 SS2 = 8 SSBetween= 42.67 a. What test are you going to perform? b. List the hypotheses c. List the decision rule d. Perform the ANOVA e. Complete the ANOVA table Source SS df MS Between Within Total f. Report your ANOVA result in APA format.
1
I conduct an online study to determine whether rewards reduce procrastination. All participants are asked to complete a task sometime before a deadline (10 days from now). The computer randomly assigns participants to one of three groups, and emails them their instructions; one group receives a reward as soon as they do the task (contingent reward); a second group receives rewards as soon as they finish the task as long as it is before the deadline (non-contingent reward) and the third group does not receive rewards at all (no reward). Three participants in the no reward condition do not complete the task, and so are dropped from analyses. The dependent variable is the amount of time (in days) it takes participants to complete the task. The JAMOVI output is attached. Post-hoc Tukey tests show that... (select all that apply) ANOVA ANOVA - Time Reward Residuals Assumption Checks Homogeneity of Variances Test (Levene's) F df1 df2 0.056 Statistic 0.964 Sum of Squares df Mean Square F…
A group of Industrial Organizational psychologists wanted to test if giving a motivational speech at the end of a meeting would encourage office workers to have a higher output to their work based on the numbers of sales each workers made. The group tested 10 participants that were in two conditions where one meeting ended in a motivational speech and another were no motivational speech was given. Here are the number of sales that was produced by the 10 participants for both conditions: Yes speech: 2, 6, 1, 9, 3, 12, 8, 0, 5, 1No speech: 3, 0, 5, 10, 1, 8, 2, 1, 9, 11Use the four steps of hypothesis testing to find out if there is a significant difference between the two groups, using APA format to answer the question.