Question

In: Statistics and Probability

A professor has noticed that, even though attendance is not a component of the final grade...

A professor has noticed that, even though attendance is not a component of the final grade for the class, students that attend regularly generally get better grades. In fact, 48% of those who come to class on a regular basis receive A's. Only 6% who do not attend regularly get A's. Overall, 60% of students attend regularly. Based on this class profile, suppose we are randomly selecting a single student from this class, and answer the questions below.

Hint #1: pretend that there are 1000 students in the class and use the values given in the problem to construct the appropriate contingency table. Round cell frequencies to the nearest integer

Hint #2: No joke, you really need to use hint #1.

Hint #3: The first step to using hint #1 is to calculate the totals for those who attend regularly and do not attend regularly.

A) P(receives A's | attends regularly) =

B) P(receives A's | does not attend regularly) =

C) P(receives A's) =

D) P(attends regularly | receives A's) =

E) P(does not attend regularly | does not receive A's) =

Solutions

Expert Solution

Let P =Probability

Attend regularly =R

Do not attend regularly =Rc

Getting A grade =A

Not getting A grade =Ac

Given:

N =Total students =1000

60% attend regularly. So, total students who attend regularly =1000*60% =600. Thus, P(R) =600/1000 =0.6

Total students who do not attend regularly =1000-600 =400. Thus, P(Rc) =400/1000 =0.4

48% of those who come to class on a regular basis receive A's:

So, P(A/R) =0.48 P(Ac/R) =1-0.48 =0.52

Only 6% who do not attend regularly get A's:

So, P(A/Rc) =0.06 P(Ac/Rc​​​​​​) =1-0.06 =0.94

A not A (Ac​​​​​​) Total
Attend regularly(R) 600*48% =288 600*52% =312 600
Do not attend regularly(Rc) 400*6% =24 400*94% =376 400
Total 312 688 1000

A) P(receives A's | attends regularly) =P(A/R) =0.48

B) P(receives A's | does not attend regularly) =P(A/Rc) =0.06

C) P(receives A's) =P(A) =312/1000 =0.312

D)

P(attends regularly | receives A's) =P(R/A) =P(A/R)*P(R)/P(A) =0.48*(600/1000)/(312/1000) =0.48*0.6/0.312 =0.9231

E)

P(does not attend regularly | does not receive A's) =P(Rc/Ac​​​​​​) =P(Ac/Rc)*P(Rc)/P(Ac) =0.94*(400/1000)/(688/1000) =0.94*0.4/0.688 =0.5465​​​​​​


Related Solutions

A professor has noticed that, even though attendance is not a component of the final grade...
A professor has noticed that, even though attendance is not a component of the final grade for the class, students that attend regularly generally get better grades. In fact, 36% of those who come to class on a regular basis receive A's. Only 4% who do not attend regularly get A's. Overall, 60% of students attend regularly. Based on this class profile, suppose we are randomly selecting a single student from this class, and answer the questions below. Hint #1:...
An instructor is interested in seeing if there is an association between attendance and final grade...
An instructor is interested in seeing if there is an association between attendance and final grade earned in a freshman level class. He records the number of absences for each student and then whether they pass or fail the class. The results are summarized below. Number of Absences 0-3 4-6 7+ Total Total 135 66 29 230 Fail 28 19 23 70 Total 163 85 52 300 Construct a 99% confidence interval for the true proportion of students who pass...
The product offers life protection, savings and even has investment component. Even though it runs for...
The product offers life protection, savings and even has investment component. Even though it runs for a specified period, life assurance companies are flexible to extend cover so that they make sure that money became available to the policyholders dependents on their death. Identify and describe the variations under this product.                            [25 marks]
Even though she has her own priorities on spending, Professor Kelton suggests that under Modern Monetary...
Even though she has her own priorities on spending, Professor Kelton suggests that under Modern Monetary Theory (MMT) the government can spent the money on anything it wants. It can spend all of its money on guns and tanks rather than on butter and classrooms. Professor Kelton posits this idea to show that MMT (the idea that government can print its own money) is neutral and viable. Do you agree?
Professor Smith wants to determine if a correlation exists between absences and final grade. She determines...
Professor Smith wants to determine if a correlation exists between absences and final grade. She determines the number of absences for ten students in her class and then determines the mean final score for those students. Below are her data: Student   Absences Score 1................. 0...........95 2................. 1.......... 90 3................. 4.......... 72 4................. 3.......... 78 5................. 2.......... 84 6................. 5.......... 67 7................. 4.......... 71 8................. 2.......... 80 9................. 7.......... 55 10............... 5 ......... 64 1. State the null hypothesis: ______________________ 2....
This is the final grade and number of absences for a set of students. Regress grade...
This is the final grade and number of absences for a set of students. Regress grade on absences. Use a 95% confidence level. Give the equation of estimation. Interpret the equation. According to the regression, now much does a tardy (= 1/2 an absence) change your grade? Evaluate the model. What evaluation criterion did you use? Could this be a case of reverse causality? If so, give an example of how the causation could run in the opposite direction. Student...
Does the location of your seat in a classroom play a role in attendance or grade?...
Does the location of your seat in a classroom play a role in attendance or grade? students in a physics course were randomly assigned to one of four groups. The 400 students in group 1 sat 0 to 4 meters from the front of the class, the 400 students in group 2 sat 4 to 6.5 meters from the front, the 400 students in group 3 sat 6.5 to 9 meters from the front, and the 400 students in group...
Good performance (obtaining a grade of A+) in this probability class depends on your attendance (A)...
Good performance (obtaining a grade of A+) in this probability class depends on your attendance (A) and completion of assignments (C). The probability that you will receive a grade of A+ are 95%, 75%, 50%, and 0%, if you attend the class and complete the assignments, if you attend but do not complete assignments, if you do not attend but complete assignments, and if you neither attend nor complete assignments, respectively. Further assume that if you attend the class, there...
A particular professor has noticed that the number of people, P, who complain about his attitude...
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: People (P) 10 12 10 10 7 6 6 3 Cups of coffee (n) 1 1 2 2 3 3 4 5 Unless otherwise stated, you can round values to two decimal places. a) Using regression to find a linear equation for...
A particular professor has noticed that the number of people, P, who complain about his attitude...
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: People (P) 11 12 10 9 6 6 6 4 Cups of coffee (n) 1 1 2 2 3 3 4 5 Unless otherwise stated, you can round values to two decimal places. Parts d), e) and g) will not be graded...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT