Chebyshev's Theorem Limit Question-Value Greater than 1

[reemsh121]

Homework Statement

According to Nielsen Media Research, kids ages 12-17 watch an average of 3 hours of tv per day. Suppose that the standard deviation is 1 hour and that the distribution of time spent watching tv has a bell-shaped distribution.

a) what percentage of kids aged 12-17 watch tv between 2 and 3 hours per day?

Homework Equations

1-1/z^2

The Attempt at a Solution

The standard deviation of 2 hours is 1, from the mean. But the value of z has to be greater than 1. With a question that has a range in it, usually means both sides will have a standard deviation from the mean. But one side is 1 and the other is the same as the mean.

So we only have one side, and I divided 1 in half to get .5 and plugged it into the formula.

1-1/.5^2

1-1/.25

1-4

-3

The answer is 34%.

I know I'm missing a step but I don't know what step. The formula is pretty straight forward and I get it, but this problem is really messing me up.

 

[diazona]

Chebyshev's inequality only makes a general statement about any probability distribution. So for example, if you plug in z = 1, you get 1-1/z^2 = 0, which means that no less than 0 of the values are more than 1 standard deviation away from the mean. But in this case, you know that the distribution is normal (a bell curve), so you can get a more precise answer, which is going to be the 34%.

As for how to get that 34%... look it up maybe? Or if you know the formula for the cumulative normal distribution (the error function), you can use that.