which of the following values is not contained within 68% of the bell-shaped curve about the mean?

Question

If the standard deviation of a set of values is 6.7 and the average value is 201.2.

Choices are ;

 

203.5

208.0

194.7

198.2

Answer 1

Lower limit should be 201.2-6.7*1=194.5

 

Upper limit should be 201.2+6.7*1=207.9

 

There is a thumb rule also that 68% of values lie within one standard deviation.

 

Answer 2

Sheily:

 

Go to either EXCEL or OPENOFFICECALC. I use the latter.  Click on f_sub_x near the top. Locate function NORMSINV.  Click next.  Enter 0.68/2 = 0.34 in the blank space after   number f_sub_x. Hit OK to get -0.4125.

 

Recall that this process is the inverse of finding the z_score for a given X value, distributed normally with mean mu and SD sigma.  The formula is z_score = (X - mu) / sigma

 

The limits of YOUR values around the mean 201.2 are Lower limit = 201.2 - (6.7)(0.4125) = 198.44 and Upper limit = 201.2 + (6.7)(0.4125) = 203.96.  The three values NOT contained in these limits are 208.0, 194.7 and 198.2