Hi Tommy,
I had a question on Guide #5, pg. 163, question 14. I just don't understand the explanation and how to come to this conclusion.
Can you please explain?
Thanks so much!
GRE Forum Archive
2 postsPage 1 of 1
- lorrainechu3
- Course Students
- Posts: 1
- Joined: Sun Apr 06, 2014 3:38 am
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Word Problem (#5), pg. 163 Q14
Hey Lorraine!
Good to see you on the forums! In the future, please include the text of any question, so that folks can see it. I'll do it here.
A biologist analyzes the number of paramecia visible under a microscope for a collection of protozoa samples. The average number of paramecia visible is 8.1 per sample, and the standard deviation of this measure is 2.4. The distribution of paramecia visible across the samples is approximately normal.
Quantity A: The number of paramecia visible at the 75th percentile in the distribution of samples
Quantity B: 10.5
So what you need to remember here is that you must know your percentages for standard deviations in normal distributions. Specifically:
1SD above and below the mean is about 68 percent.
2SD above and below the mean is about 95 percent.
3SD above and below the mean is 100 percent.
That means, if we want to find something 1SD above the mean, we would include 34 percent of people (half of 68). In this case, 1SD above the mean is 10.5 (Because 8.1 is our mean, and our standard deviaion is 2.4). We know this would correspond to about the 84th percentile (50th percentile is the mean, and 1SD above the mean is 34 percent). So the 84th percentile has 10.5 paramecia per sample. That means the 75th percentile would have fewer paramecia per sample. That means Quantity B is bigger.
Hope that was helpful! (I know it's not much different from what the book says, but there aren't a lot of ways to go at this one. Hopefully my language was clearer, but let me know if not!).
-t
Good to see you on the forums! In the future, please include the text of any question, so that folks can see it. I'll do it here.
A biologist analyzes the number of paramecia visible under a microscope for a collection of protozoa samples. The average number of paramecia visible is 8.1 per sample, and the standard deviation of this measure is 2.4. The distribution of paramecia visible across the samples is approximately normal.
Quantity A: The number of paramecia visible at the 75th percentile in the distribution of samples
Quantity B: 10.5
So what you need to remember here is that you must know your percentages for standard deviations in normal distributions. Specifically:
1SD above and below the mean is about 68 percent.
2SD above and below the mean is about 95 percent.
3SD above and below the mean is 100 percent.
That means, if we want to find something 1SD above the mean, we would include 34 percent of people (half of 68). In this case, 1SD above the mean is 10.5 (Because 8.1 is our mean, and our standard deviaion is 2.4). We know this would correspond to about the 84th percentile (50th percentile is the mean, and 1SD above the mean is 34 percent). So the 84th percentile has 10.5 paramecia per sample. That means the 75th percentile would have fewer paramecia per sample. That means Quantity B is bigger.
Hope that was helpful! (I know it's not much different from what the book says, but there aren't a lot of ways to go at this one. Hopefully my language was clearer, but let me know if not!).
-t
2 posts Page 1 of 1