Question

A professor knows that her statistics students' final test scores have a mean of 75 and a standard deviation of 8.3. In her class, an "A" is any test score of 90 or higher. This quarter she has 26 students in her class. What is the probability that 3 students or more will score an "A" on the final test? Hint: You will need to use your knowledge of normal probability distributions to determine the probability of one individual getting an A and then use your knowledge of binomial distributions to determine the probability of 3 students or more out of 26 students getting an A.

          A professor knows that her statistics students' final
test scores have a mean of 75 and a standard deviation of 8.3.
In her class, an "A" is any test score of 90 or higher. This
quarter she has 26 students in her class. What is the probability
that 3 students or more will score an "A" on the final test?
Hint: You will need to use your knowledge of normal probability
distributions to determine the probability of one individual
getting an A and then use your knowledge of binomial distributions
to determine the probability of 3 students or more out of 26
students getting an A.
        
Show more…

Added by Rocio D.

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
A professor knows that her statistics students' final test scores have a mean of 75 and a standard deviation of 8.3. In her class, an "A" is any test score of 90 or higher. This quarter she has 26 students in her class. What is the probability that 3 students or more will score an "A" on the final test? Hint: You will need to use your knowledge of normal probability distributions to determine the probability of one individual getting an A and then use your knowledge of binomial distributions to determine the probability of 3 students or more out of 26 students getting an A.
Close icon
Play audio
Feedback
Powered by NumerAI
Kathleen Carty David Collins
Danielle Fairburn verified

Sri K and 90 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
a-professor-knows-that-her-statistics-students-final-grade-scores-have-a-mean-of-75-and-a-standard-deviation-of-82-in-her-class-an-a-is-any-test-score-of-90-or-higher-this-quarter-she-has-25-66592

A professor knows that her statistics students' final grade scores have a mean of 75 and a standard deviation of 8.2. In her class, an "A" is any test score of 90 or higher. This quarter she has 25 students in her class. What is the probability that 3 students or more will score an "A" on the final test

Madhur L.

a-professor-knows-that-her-statistics-students-final-exam-scores-have-a-mean-of-75-and-a-standard-deviation-of-106-in-his-class-an-a-is-any-exam-score-of-90-or-higher-this-quarter-she-has-23-12016

A professor knows that her statistics students' final exam scores have a mean of 75 and a standard deviation of 10.6. In her class, an "A" is any exam score of 90 or higher. This quarter she has 23 students in her class. What is the probability that 4 students or more will score an "A" on the final exam? prob = ___________________ Report your final answer accurate to 4 decimal places. Do not round any of the numbers in this calculation until the very end of the problem!

Madhur L.

a-professor-knows-that-her-statistics-students-final-exam-scores-have-a-mean-of-75-and-a-standard-deviation-of-101-in-his-class-an-a-is-any-exam-score-of-90-or-higher-this-quarter-she-has-23-students-

A professor knows that her statistics students' final exam scores have a mean of 75 and a standard deviation of 10.1. In his class, an "A" is any exam score of 90 or higher. This quarter she has 23 students in her class. What is the probability that 4 students or more will score an "A" on the final exam?

Christopher D.


*

Recommended Textbooks

-
Elementary Statistics a Step by Step Approach

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition
achievement 1,953 solutions
The Practice of Statistics for AP

The Practice of Statistics for AP

Daren S. Starnes, Daniel S. Yates, David S. Moore 4th Edition
achievement 1,411 solutions
Introductory Statistics

Introductory Statistics

Barbara Illowsky, Susan Dean 1st Edition
achievement 1,990 solutions

*

Transcript

-
00:01 Hello, let's have a look on the question.
00:02 So it is given to us that mu, that is me, is equal to 75.
00:06 And the standard deviation sigma is equal to 8 .3.
00:11 So for the a part, here we are using normal probability distribution, normal distribution.
00:24 So probability that x will be greater than equal to 90 will be equal to probability that x minus mu divided by sigma is greater than, now we can put all the values for x, mu and sigma.
00:41 So this is 90 minus mu is 75 divided by 8 .3.
00:46 So this will be equal to, this is the value of z.
00:49 So probability z is greater than 1 .81.
00:53 This will be equal to 0 .0352.
00:57 This value is from z table.
01:04 Next, b part by using binomial distribution.
01:13 Binomial distribution.
01:18 So, px for binomial distribution is given by the formula ncx, p to the power x, q to the power n minus x...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever