Question

Facespace is a popular form of social media. Recent reports show that the mean time spent on Facespace is 35 minutes a day with a standard deviation of 6 minutes a day. The data is normally distributed. If 1100 people are on in one sitting, how many of them lie within one standard deviation below the mean and two standard deviations above the mean?

Answer 1

897

Explanation:

I think it deleted my prior solution because I linked the Wikipedia article for the empirical rule... So to retype this:

We'll be using the empirical, or 68-95-97.5 rule of normal distributions which says that 68% of data in a normal distribution is within 1 standard deviation, 95% is within two, and 97.5% is within three. Graphical representations of the rule can be found online and may be helpful to understand it more easily.

The first part of the problem is relatively straightforward, to get the two pieces within one standard deviation, that's 68% of the total population of 1100. So, 0.68*1100=748.

The second part is a bit trickier, since it is just the part of the second standard deviation out that is above the mean. To get this, we need to think about the difference between one standard deviation out and two, percentage-wise. Since two standard deviations out is 95% of the data, the difference between one and two is 95%-68%, or 27% of the data. However, since we only want the upper half of that, we'll just be using 13.5%. So our second piece is 13.5% of 1100, or 148.5.

Add together our two pieces, 748+148.5=896.5 and round up to 897.