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A biologist analyzes the number of paramecia visible under a microscop
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18 Jan 2023, 05:56
18 Jan 2023, 05:56
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Question Stats:
66% (02:03) correct
33% (01:15) wrong based on 6 sessions
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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
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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
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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.
