Standard Deviation Word Problem

[kwikness]

Homework Statement

It has been projected that the average and standard deviation of the amount of time spent online using the Internet are, respectively, 14 and 17 hours per person per year (approximately normally distributed). What value is exactly 1 standard deviation below the mean?

Homework Equations

Emiprical Rule
$$\mu \pm \sigma$$ contains approximately 68% of the measurements.
$$\mu \pm 2\sigma$$ contains approximately 95% of the measurements.
$$\mu \pm 3\sigma$$ contains approximately almost all of the measurements.

The Attempt at a Solution

In similar problems, the mean is the larger number in the problem, so solving the problem is a simple matter of subtracting the standard deviation from the mean to find out the percentage of population.

In this case though, the standard deviation (17) is greater than the mean(14)? If I solve this like I do normal problems, this would leave me with a negative value for time spent on the Internet.

Is this an error in the textbook or is there something I'm missing here?

 

[jambaugh]

My guess is that the problem is meant to emphasize the shortcomings of assuming a normal distribution, e.g. the normal distribution spans the entire real line while examples may have a restricted domain, as in this case only positive reals.

 

[kwikness]

Thanks

 

[statdad]

It should be used to reinforce the idea that assuming things are normally distributed isn't always justified: the actual question as you describe it shows that the times can't be normal, for the reason you point out.