The mean length of Beethoven’s nine symphonies is 37 minutes; the standard deviation is 12 minutes.. All of the following data values lie within how many standard deviations of the mean? 27 min, 30 min, 47 min, 35 min, 30 min, 40 min, 35 min, 22 min, 65 min

Question

The mean length of Beethoven’s nine symphonies is 37 minutes;  the standard deviation is 12 minutes.. All of the following data values lie within how many standard deviations of the mean? 27 min, 30 min, 47 min, 35 min, 30 min, 40 min, 35 min, 22 min, 65 min

whpalmer4 · Answer

If the mean is 37 and the std dev is 12, then the range encompassed by 1 std dev. from the mean would be 37-12 to 37+12 or 25 to 49.

extend the pattern for 2 std dev's and 3 std dev's and see how many you need to get all of the values covered.

by the way, that data is kind of bogus — there is no "fixed length" of any of his symphonies; the durations vary substantially!  For example, the 9th symphony, here listed as being 65 minutes in length, has been recorded at durations varying from 60 minutes to over 79 minutes!