GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 28Live Online Class with Top GRE Expert Mike Butville
08:00 PM EDT
-10:00 PM EDT
Top scores are possible when you enroll in a powerful GRE course, taught live online + 6 months access to TTP GRE OnDemand video courses included! Class starts Mon/Wed Sept. 28, 2026 - Dec. 9, 2026, 8:00pm-10:00pm EST
A biologist analyzes the number of paramecia visible under a microscop
[#permalink]
18 Jan 2023, 05:56
18 Jan 2023, 05:56
Expert Reply
1
Bookmarks
00:00
Question Stats:
66% (02:03) correct
33% (01:15) wrong based on 6 sessions
Hide Show timer Statistics
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.
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
The number of paramecia visible at the \(75^{th}\) percentile in the distribution of samples |
10.5 |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: A biologist analyzes the number of paramecia visible under a microscop
[#permalink]
18 Jan 2023, 11:26
18 Jan 2023, 11:26
1
Going by the formula,
Percentile Value = μ + zσ, where
μ = Mean
z = Z value
σ = Standard Deviation
and knowing that z value of 1 is roughly near 84th percentile, 75 percentile will definitely < 1
Hence, 8.1 + (z)*2.4, where z < 1 will definitely be lesser than 10.5, hence B
Percentile Value = μ + zσ, where
μ = Mean
z = Z value
σ = Standard Deviation
and knowing that z value of 1 is roughly near 84th percentile, 75 percentile will definitely < 1
Hence, 8.1 + (z)*2.4, where z < 1 will definitely be lesser than 10.5, hence B
Re: A biologist analyzes the number of paramecia visible under a microscop
[#permalink]
20 Jan 2023, 05:00
20 Jan 2023, 05:00
Expert Reply
OE
The 75 percentile of an approximately normally distributed variable is just shy of 1 standard deviation higher than the mean. (About 2/3 of all observations fall within 1 standard deviation of the mean, so 1 standard deviation above the mean lies at approximately the 50 percentile = 100*1/2*1/3=83 percentile.
Quantity B is 10.5 - 8.1 = 2.4 units above the mean, or exactly 1 standard deviation above the mean. Therefore, Quantity B is greater.
The 75 percentile of an approximately normally distributed variable is just shy of 1 standard deviation higher than the mean. (About 2/3 of all observations fall within 1 standard deviation of the mean, so 1 standard deviation above the mean lies at approximately the 50 percentile = 100*1/2*1/3=83 percentile.
Quantity B is 10.5 - 8.1 = 2.4 units above the mean, or exactly 1 standard deviation above the mean. Therefore, Quantity B is greater.
