How do I calculate a percentage that lies above, below, or in between a particular standard deviation?

For example: The mean is 205, standard deviation is 30. What % lies below 250? I know that it is 1.5 standard deviations from the mean but I don't know how to turn that into a % of the normal distribution.



ThanksHow do I calculate a percentage that lies above, below, or in between a particular standard deviation?
Look for a z-score of 1.50 in standard normal tables, or use one of the online calculators such as http://stattrek.com/Tables/normal.aspx, which does not require you to convert to standard normal).



My book gives 0.9332; the aforementioned calculator gives 0.93319. So roughly 93% lies below 250.



For the other forms:



P(X %26gt; x) = 1 - P(X %26lt; x)

P(x1 %26lt; X %26lt; x2) = P(X %26lt; x2) - P(X %26lt; x1)