I have summery data from a recent Statistics class, but much of the actual data has been lost.
On the eight exam, I seem to recall that the scores were distributed in a roughly-symmetric generally bell-shaped fashion. The mean score was 81 and the standard deviation was 7. About what portion of the students had scores between 67 and 95?

Question

I have summery data from a recent Statistics class, but much of the actual data has been lost. 
On the eight exam, I seem to recall that the scores were distributed in a roughly-symmetric generally bell-shaped fashion. The mean score was 81 and the standard deviation was 7. About what portion of the students had scores between 67 and 95?

kropot72 · Answer

The 'empirical rule' for a Normal Distribution can be used to solve this.

anonymous · Answer

That's the same as Chebyshev's Theorem, correct?

anonymous · Answer

Yea it is

anonymous · Answer

Okay. I should be able to figure it out now. Thank you, guys!

kropot72 · Answer

You don't have to use Chebyshev's Theorem, the reason being that it is given that the distribution is approximately Normal. When you find the number of standard deviations the given scores are from the mean, the solution can be read directly from the graph that I posted above.

anonymous · Answer

I'm a bit confused again. I'm sorry. I can read the answer from the graph you posted?

kropot72 · Answer

The standard deviation is 7. Two standard deviations are 7 * 2 = 14.
81 + 14 = ?
81 - 14 = ?

anonymous · Answer

95 and 67.

anonymous · Answer

yes

anonymous · Answer

Is that the answer? I had 81-2*7 & 81+2*7 down on my paper but for some reason I thought there was more to the problem.