Question

In: Statistics and Probability

A professor is studying to see if there is a relationship between the grades and gender...

A professor is studying to see if there is a relationship between the grades and gender of his students. He picks a random sample of his students and notes their grades (A, B, or C) and their gender (male or female). He finds that:

  1. 28% are A students.
  2. 58% are B students.
  3. 62% of his students are female.
  4. Of those who are female, one-third are A students.
  5. Of those who are B students, three-fifths are female students.

What percentage of the students are male and have a C grade?

Solutions

Expert Solution

We know the following probabilities

28% are A students.

A randomly selected student has an A grade is

58% are B students.

A randomly selected student has a B grade is

A randomly selected student has a C grade is (Only A,B, or C grades are given)

62% of his students are female.

A randomly selected student is a female is

A randomly selected student is a male is

Of those who are female, one-third are A students.

Of those who are B students, three-fifths are female students

The probability that a randomly selected student is female and has an A grade is

The probability that a randomly selected student is female and has a B grade is

Using the law of total probabilities we can get the probability that a randomly selected student is female and has a C grade using

Using the law of total probabilities again, we can get the probability that a randomly selected student is male and has a C grade using

ans: The percentage of the students are male and have a C grade is 7.47%


Related Solutions

A professor is studying to see if there is a relationship between the grades and gender...
A professor is studying to see if there is a relationship between the grades and gender of his students. He picks a random sample of his students and notes their grades (A, B, or C) and their gender (male or female). He finds that: 28% are A students. 58% are B students. 62% of his students are female. Of those who are female, one-third are A students. Of those who are B students, three-fifths are female students. What percentage of...
Imagine a professor wants to examine if there is a relationship between gender and performance on...
Imagine a professor wants to examine if there is a relationship between gender and performance on a writing test. Thirty girls and thirty boys participated in his experiment. They were given a standard writing test and their grades were given as “outstanding”, “good”, “passing”, and “failing”. If the professor decided to use a Chi-square test to examine the relationship, how many degrees of freedom are there in this Chi-square test? When using the Chi-square test, the probability of Type I...
A marketing professor at Givens College is interested in the relationship between hours spent studying and...
A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter are in file HoursPts.xlsx. Hours Points 45 40 30 35 90 75 60 65 105 90 65 50 90 90 80 80 55 45 75 65 a) Use XLSTAT to create a scatterplot with hours spent studying on the horizontal axis and total points earned on the...
A marketing professor at Givens College is interested in the relationship between hours spent studying and...
A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow. Hours Spent Studying Total Points Earned 45 40 30 35 90 75 60 65 105 90 65 50 90 90 80 80 55 45 75 65 (a) Develop an estimated regression equation showing how total points earned can be predicted from hours spent studying. (Round your...
Is there a relationship between handedness and gender?
  Is there a relationship between handedness and gender? A researcher collected the following data in hopes of discovering if handedness and gender are independent (Ambidextrous individuals were excluded from the study). Use the Chi-Square test for independence to explore this at a level of significance of 0.05.   Left-Handed Right-Handed Men 13 22 Women 27 18
A researcher wants to see if there are any differences between three types of studying: Studying...
A researcher wants to see if there are any differences between three types of studying: Studying in a quiet room, studying in a room with classical music playing, and studying in a room with loud lawn equipment going on outside the window. She recruits 9 college students and puts three in each group. She has them read an excerpt from a physics textbook and then gives them a 5-question quiz. Below are their scores. Does study condition have an effect...
There is a lot of interest in the relationship between studying music and studying math. We...
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Here are the Math SAT scores from 9 students who studied music through high school and 10 students who did not. The degrees of freedom (d.f.) is given to save calculation time if you are not using software. Math SAT Scores mean ?2s2 ?s Music (x1) 627 625 605 568 567 619 548 638...
There is a lot of interest in the relationship between studying music and studying math. We...
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Here are the Math SAT scores from 9 students who studied music through high school and 10 students who did not. The degrees of freedom (d.f.) is given to save calculation time if you are not using software. Math SAT Scores mean ?2s2 ?s Music (x1) 627 625 605 568 567 619 548 638...
There is a lot of interest in the relationship between studying music and studying math. We...
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level. The 8...
I have tables student, professor, and person. The relationship between student and person, and professor and...
I have tables student, professor, and person. The relationship between student and person, and professor and person is Is A inheritance. A person may be a student but not a professor, a professor but not a student, or neither a professor or a student. How do I write a trigger in SQL that forces the constraint that a person cannot be a student and a professor. Some extra info: I have defined ID to be PK of person. ID is...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT