Question

In: Statistics and Probability

In a large introductory statistics lecture​ hall, the professor reports that 53​% of the students enrolled...

In a large introductory statistics lecture​ hall, the professor reports that 53​% of the students enrolled have never taken a calculus​ course, 28​% have taken only one semester of​ calculus, and the rest have taken two or more semesters of calculus. The professor randomly assigns students to groups of three to work on a project for the course. You are assigned to be part of a group. What is the probability that of your other two​ groupmates,

​a) neither has studied​ calculus?

​b) both have studied at least one semester of​ calculus?

​c) at least one has had more than one semester of​ calculus?

Solutions

Expert Solution

As the students are randomly assigned to each group , thus event of of taking calculus course is independent of each other.

P( never taken Calculus) =0.53

P( one semester of Calculus) = 0.28

P( two or more semester of Calculus) = 0.19

a) P( neither has studied Calculus) = P( both never taken Calculus)

As events are independent

P( neither has studied Calculus) = 0.53 *0.53 = 0.2809

b) P( both have studied at least one semester of Calculus)

= P( both have studied one semester of Calculus) + P( both have studied two or more semester of Calculus)

+ P( either of them have studied one semester of Calculus and another two or more semester of Calculus)

= 0.28 *0.28 + 0.19*0.19 +2 *0.28*0.19

= 0.2209

c) P( atleast one have studied more than one semester of Calculus)

= P( either of them have studied two or more semester of Calculus and another one not  )

+ P( both of them have studied two or more semester of Calculus )

= 2*0.19*(1-0.19 ) + 0.19*0.19

= 0.3439

Note : IF events A and B are independent

P( AB) =P( A ) *P( B)

Note : To find the following probabilities we multiplied by two , as the event can happen two ways

first person have studied one semester of Calculus and second two or more semester of Calculus

or

first person have studied wo or more semester of Calculus and second one semester of Calculus

P( either of them have studied one semester of Calculus and another two or more semester of Calculus)

= 0.19*0.28 +0.28 *0.19

Similarly

P( either of them have studied two or more semester of Calculus and another one not  )


Related Solutions

In a large class of introductory Statistics​ students, the professor has each person toss a coin...
In a large class of introductory Statistics​ students, the professor has each person toss a coin 29 times and calculate the proportion of his or her tosses that were heads. Complete parts a through d below. The Independence Assumption (is or is not) )_____satisfied because the sample proportions (are or are not)_____independent of each other since one sample proportion (can affect or does not affect)______another sample proportion. The​Success/Failure Condition is not satisfied because np=____ and nq=____which are both (less than...
COIN TOSSES In a large class of introductory Statistics students, the professor has each student toss...
COIN TOSSES In a large class of introductory Statistics students, the professor has each student toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions. What shape would you expect this histogram to be? Why? Where do you expect the histogram to be centred? How much variability would you expect among these proportions? Explain why a Normal...
A professor who teaches a large introductory statistics class (197 students) with eight discussion sections would...
A professor who teaches a large introductory statistics class (197 students) with eight discussion sections would like to test if student performance differs by discussion section, where each discussion section has a different teaching assistant. The summary table below shows the average score for each discussion section as well as the standard deviation of scores and the number of students in each section. Sec 1 Sec 2 Sec 3 Sec 4 Sec 5 Sec 6 Sec 7 Sec 8 ni...
Students enrolled in an introductory statistics course at a university were asked to take a survey...
Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student’s learning style was more visual or verbal. Each student received a numerical score ranging from -11 to +11. Negative scores indicated a visual learner, and positive scores indicated a verbal learner. The closer the score was to -11 or +11, the stronger the student’s inclination toward that learning style. A score of 0 would indicate neutrality between visual or...
Students enrolled in an introductory statistics course at a university were asked to take a survey...
Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student’s learning style was more visual or verbal. Each student received a numerical score ranging from -11 to +11. Negative scores indicated a visual learner, and positive scores indicated a verbal learner. The closer the score was to -11 or +11, the stronger the student’s inclination toward that learning style. A score of 0 would indicate neutrality between visual or...
Students enrolled in an introductory statistics course at a university were asked to take a survey...
Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student’s learning style was more visual or verbal. Each student received a numerical score ranging from -11 to +11. Negative scores indicated a visual learner, and positive scores indicated a verbal learner. The closer the score was to -11 or +11, the stronger the student’s inclination toward that learning style. A score of 0 would indicate neutrality between visual or...
A professor using an open source introductory statistics book predicts that 60% of the students will...
A professor using an open source introductory statistics book predicts that 60% of the students will purchase a hard copy of the book, 25% will print it out form the web, and 15% will read in online. At the end of the semester he asks his students to complete a survey where they indicate what format of the book they used. Of the 126 students, 71 said they bought a hard copy of the book, 30 said they printed it...
A professor using an open source introductory statistics book predicts that 60% of the students will...
A professor using an open source introductory statistics book predicts that 60% of the students will purchase a hard copy of the book, 25% will print it out from the web, and 15% will read it online. At the end of the semester he asks his students to complete a survey where they indicate what format of the book they used. Of the 126 students, 73 said they bought a hard copy of the book, 30 said they printed it...
1) A professor using an open-source introductory statistics book predicts that 60% of the students will...
1) A professor using an open-source introductory statistics book predicts that 60% of the students will purchase a hard copy of the book, 25% will print it out from the web, and 15% will read it online. At the end of the semester she asks her students to complete a survey where they indicate what format of the book they used. Of the 126 students, 71 said they bought a hard copy of the book, 30 said they printed it...
1. A professor using an open source introductory statistics book predicts that 10% of the students...
1. A professor using an open source introductory statistics book predicts that 10% of the students will purchase a hard copy of the book, 55% will print it out from the web, and 35% will read it online. At the end of the semester he asks his students to complete a survey where they indicate what format of the book they used. Of the 200 students, 25 said they bought a hard copy of the book, 85 said they printed...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT