Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5. What value is exactly 2 standard deviations less than the mean?
10.5, 11, 11.5, 12, 12.5
Arithmetic mean and standard deviation
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10.5, one SD away means +/- SD so 2 less means: 13.5-3vaibhav.iit2002 wrote:Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5. What value is exactly 2 standard deviations less than the mean?
10.5, 11, 11.5, 12, 12.5
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Mean is 13.5
SD = 1.5
2sd = 2* 1.5 = 3
We need to find the value exactly 2 sd less than the mean so we need to find 13.5-3
If we had to find the value exactly 2 sd greater than the mean we would do 13.5+3
In general :
Points k Sd above the mean : x+k*SD
points k sd below the mean : x-k*SD
SD = 1.5
2sd = 2* 1.5 = 3
We need to find the value exactly 2 sd less than the mean so we need to find 13.5-3
If we had to find the value exactly 2 sd greater than the mean we would do 13.5+3
In general :
Points k Sd above the mean : x+k*SD
points k sd below the mean : x-k*SD