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20 Jul 2021, 02:30
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A
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The arithmetic mean and standard deviation of a certain normal distribution are \(\frac{5}{6}\) and \(\frac{1}{3}\), respectively. What value is exactly \(2 \frac{1}{2}\) standard deviations less than the mean?
A. 0
B. 1/12
C. 1/6
D. 1/4
E. 1/3
A. 0
B. 1/12
C. 1/6
D. 1/4
E. 1/3
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20 Jul 2021, 11:26
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Bunuel
Standard Deviation(SD) = 1/3
\(2 \frac{1}{2}\) = 5/2 standard deviations
So, 1/3 * 5/2 = 5/6
Therefore, 5/2 deviations less than mean = 5/6 - 5/6 = 0, IMO, (A)!
20 Jul 2021, 16:21
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Hey guys
I had the worst statistics teacher ever in grad school so I'll try to make this painless
A standard deviation is how far from the average you move
All you have to know for this problem is that when you go one standard deviation down from the mean you subtract one standard deviation from the mean, that's it
The mean is \(\frac{5}{6}\)
One standard deviation is \(\frac{1}{3}\)
Let's make the denominator 6 because the mean has 6 in the denominator
\(\frac{1}{3} = \frac{2}{6}\)
One standard deviation is \(\frac{2}{6}\)
So what value is 2.5 standard deviations (SD) from the mean?
Mean - One SD =
\(\frac{5}{6} - \frac{2}{6} = \frac{3}{6}\)
Now let's subtract another one:
\(\frac{3}{6} - SD = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}\)
Now we have to subtract half of a standard deviation
What is one half of \(\frac{2}{6}\)?
\(\frac{2}{6} * \frac{1}{2} = \frac{2}{12} = \frac{1}{6}\)
\(\frac{1}{6} - \frac{SD}{2}\) = \(\frac{1}{6} - \frac{1}{6}\) = 0
The answer is (A)
I had the worst statistics teacher ever in grad school so I'll try to make this painless
A standard deviation is how far from the average you move
All you have to know for this problem is that when you go one standard deviation down from the mean you subtract one standard deviation from the mean, that's it
The mean is \(\frac{5}{6}\)
One standard deviation is \(\frac{1}{3}\)
Let's make the denominator 6 because the mean has 6 in the denominator
\(\frac{1}{3} = \frac{2}{6}\)
One standard deviation is \(\frac{2}{6}\)
So what value is 2.5 standard deviations (SD) from the mean?
Mean - One SD =
\(\frac{5}{6} - \frac{2}{6} = \frac{3}{6}\)
Now let's subtract another one:
\(\frac{3}{6} - SD = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}\)
Now we have to subtract half of a standard deviation
What is one half of \(\frac{2}{6}\)?
\(\frac{2}{6} * \frac{1}{2} = \frac{2}{12} = \frac{1}{6}\)
\(\frac{1}{6} - \frac{SD}{2}\) = \(\frac{1}{6} - \frac{1}{6}\) = 0
The answer is (A)
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
