Question

A random sample of 45 internet videos is selected from a large library where the average length is 14 minutes with a standard deviation of 3.3 minutes. How likely is it for the sample mean to be between 15 and 20 minutes? Round to 3 decimal places. 

          A random sample of 45 internet videos is selected from a large library where the average length is 14 minutes with a standard deviation of 3.3 minutes. How likely is it for the sample mean to be between 15 and 20 minutes? Round to 3 decimal places.
Show more…

Added by Xavier J.

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 random sample of 45 internet videos is selected from a large library where the average length is 14 minutes with a standard deviation of 3.3 minutes. How likely is it for the sample mean to be between 15 and 20 minutes? Round to 3 decimal places.
Close icon
Play audio
Feedback
Powered by NumerAI
Danielle Fairburn Jennifer Stoner
Ivan Kochetkov verified

Ahmet Yavas and 96 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

-
the-average-video-length-is-154-minutes-long-with-a-population-deviation-of-16-minutes-6-what-is-the-probability-that-the-mean-of-a-random-sample-of-16-videos-is-shorter-than-15-minutes-6-wh-10397

The average video length is 15.4 minutes long, with a population deviation of 1.6 minutes. (6) What is the probability that the mean of a random sample of 16 videos is shorter than 15 minutes? (6) What is the probability of a single video being shorter than 15 minutes? (3) Is it unusual to have a video that is 15 minutes long? Justify your answer.

Ahmet Y.
the-running-time-for-videos-submitted-to-youtube-in-a-given-week-is-normally-distributed-with-390-seconds-and-standard-deviation-148-seconds-if-a-single-video-is-randomly-selected-what-is-th-18575

'The running time for videos submitted to YouTube in a given week is normally distributed with / = 390 seconds and standard deviation 148 seconds If a single video is randomly selected, what is the probability that the running time of the video exceeds 6 minutes (360 seconds)? Suppose that a sample of 40 videos is selected: What is the probability that the mean running time of the sample exceeds 6 minutes?'

Michael N.
a-family-watches-netflix-on-average-of-3-hours-a-day-the-standard-deviation-is-45-minutes-what-is-the-probability-that-netflix-is-watched-between-22-and-35-hours

A family watches Netflix on average of 3 hours a day, the standard deviation is 45 minutes. What is the probability that Netflix is watched between 2.2 and 3.5 hours?

Ajiboye T.
*

Recommended Textbooks

-
Elementary Statistics a Step by Step Approach

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition
achievement 1,238 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 1,592 solutions
Introductory Statistics

Introductory Statistics

Barbara Illowsky, Susan Dean 1st Edition
achievement 1,721 solutions
*

Transcript

-
00:01 There is given a mean and the standard deviation here.
00:03 So the average video length, which is the population mean denoted by mu that was given as 15 .4 and the population deviation means the population standard deviation which is given as 1 .6 here so the sample size given here, which is the sample size is 16 here so first of all, we have to find the probability for the sample.
00:26 So what i need i need the sample mean the sample mean is the same with the population mean which is 15 .4 and also i need the sample standard deviation sample standard deviation, which is the population standard division divided by square root of the sample size so the population the sample standard division, which is 1 .6 divided by root 16 that would be 0 .4 here so i can define the random variable x bar for the sample normally distributed the mean is 15 .4 in the standard division 0 .4 here so this is shorter than if this is shorter than 15 we have to find this probability here at this step i'm gonna use the normal cdf function there is no in a lower boundary put very small number upper boundary is 15 and the mean is 15 .4 and the standard division 0 .4 press second variance and the normal cdf lower boundary this is negative 1 second a99 and the upper boundary is 15 and the mean is 15 .4 in the standard division 0 .4 here so the answer would be which is 0 .15 and 87 here and the next part of the question if you just select a single video, right? so we have to use the population random variable x here which is normally distributed the mean and the standard division here so in this case, we're gonna find shorter than so the x is shorter than 15...
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
Join the community

18,000,000+

Students on Numerade

Trusted by students at 8,000+ universities

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