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The average number of hours that a kid spends per day working at  a computer 3.5 hours. This distribution is normally distributed with the STDV of 0.9 hours. What percentage of kids spend more than 3.8 hours per day working at a computer? 

Mar 14th, 2015

To solve this, one must read up on Gaussian Normal Distribution, e.g.:

http://en.wikipedia.org/wiki/Error_function

1.0-0.5*erfc((3.5-3.8)/(sqrt(2)*0.9)) = 0.369... = 36.9%

Sanity check: Average is 3.5h, so 50% of kids spend less than 3.5h, 50% spend more (with Gaussian distribution mean and median are the same). That means that more than 50% of kids will spend LESS than 3.8h, and less than 50% of kids will spend MORE than 3.8h.

More details:

The term A=0.5*erfc() is the cumulative probability yp to that point (from -infinity). Since we want to know the probability from the point to +infinity, we must take 1-A.

Mar 14th, 2015

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