[Alex]

Originally Posted by BarTopDancer

The mean is 80. The standard deviation is 6. You have to take the Mean ± 2(SD). So 80 ± 2*6 = the answer.

This is correct.

The empirical rule is 68-95-99.7, right? That means that for a normal distribution, one standard deviation will include about 68% of the population. Go out to 2 standard deviations and it will include about 95% of the population. 3 standard deviations takes you up to 99.7% of the population.

So, since the question asks about covering 95% of the results, that would be two standard deviations. That's the reasoning underlying the correct formula you gave. So Answer B (68 to 92) is correct.

Part 2.

I have no idea. I am so lost again.

You're correct that 3 standard deviations is ±18 points from the mean (62 to 98). And 5 standard deviations would be ±30 points.

Per the empirical rule, 99.7% of all results will be within just 3 standard deviations of the mean. So we know that only 0.3% of all results will be lower than 62 points or higher than 98 points.

I don't know if it is covered by your textbook but if you extend the empirical rule you get:

1 standard deviation = 68%
2 standard deviation = 97%
3 standard deviation = 99.7%
4 standard deviation = 99.99%
5 standard deviation = 99.9999% of all results

So, since a score of 50 is 5 standard deviations away from the mean, you would expect only 0.0001% of scores to be that far from the mean. Another way of saying that is you'd expect one student out of a million to score that low. Since it is extremely unlikely that a million students are taking the Stats 100 class you would not expect that anybody will score that low (though it remains statistically possible it is statistically improbable).