The arithmetic mean and standard deviation of a certain normal distrib

Question

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

Showmeyaa · Answer

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)!

PolarisTestPrep · Answer

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)

The arithmetic mean and standard deviation of a certain normal distrib

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