Question
upstudy study bank question image url

A teacher brings a bag of marbles containing 600 white marbles and 200 red marbles. She asks her students to determine how many red marbles are in the bag without counting them. A student randomly draws 200 marbles from the bag. Of the 200 marbles, 47 are red. (a) Identify the population. The 200 white marbles The 800 marbles The 200 marbles The 47 red marbles (b) What proportion of the population is red? When writing a fraction, remember to avoid spaces. For example: \( 1 / 2 \).

Ask by Mitchell Washington. in the United States
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

**(a) Identify the population** - The population is all the marbles in the bag, totaling \(800\) marbles. **(b) Proportion of the population that is red** - The proportion of red marbles is \( \frac{1}{4} \).

Solution

**(a) Identify the population** - The population is all the marbles in the bag. - The bag contains \(600\) white marbles and \(200\) red marbles. - Therefore, the population is \(600 + 200 = 800\) marbles. **Answer:** The population is the \(800\) marbles. **(b) Proportion of the population that is red** - There are \(200\) red marbles in the bag. - The total number of marbles is \(800\). - The proportion of red marbles is given by \[ \frac{200}{800} \] - Simplifying the fraction: \[ \frac{200}{800} = \frac{200 \div 200}{800 \div 200} = \frac{1}{4} \] **Answer:** The proportion of red marbles is \( \frac{1}{4} \).

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Mind Expander

The population in this scenario is the total collection of marbles in the bag, which includes both white and red marbles, making it the 800 marbles. To find the proportion of the population that is red, you divide the number of red marbles drawn (47) by the total number of marbles drawn (200). So, the proportion is \( 47 / 200 \). For a bit of fun, did you know that marbles have been around since ancient times? They were made from a variety of materials, including clay, stone, and glass, and they’ve evolved into the bright, colorful spheres we see today! Speaking of drawing marbles, a common mistake is assuming that each draw is independent when sampling from a small population. If your sample size is a significant fraction of the total population, the remaining marbles are not truly representative, which can skew your results! Always consider the size of your sample in relation to the total!

Related Questions

Latest Statistics Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy