After preparing the results of their measurement of the weight of children that participated in their pediatric study, Steph's graduate assistant spilled coffee on their papers. If Steph is able to read that 50 lbs is the third standard deviation to the left of the mean, and 110 lbs also falls on a standard deviation, then which of the following could be the mean weight of the children in the study, assuming regular distribution? Indicate all possible values.
a. 80
b. 85
c. 86
d. 95
e. 100

• ANSWERS: a,c,d
  Explanation:
  Let mean= x
  standard deviation= d
  Given 50 is the 3rd standard deviation to left of mean,
  this means x-3d=50 -----------eqn(1)
  Also it is given that 110 falls on some standard deviation.
  Generally it is known that all values lie within 3 standard deviations from mean.
  Considering all the possible cases,
  Case i:
  110 is the 2nd standard deviation to left of mean
  x-2d=110
  solving this with eqn(1) we get d=60, x=230
  Case ii:
  110 is the 1st standard deviation to left of mean
  x-d=110
  solving this with eqn(1) we get d=30, x=140
  Case iii:
  110 is the 1st standard deviation to right of mean
  x+d=110
  solving this with eqn(1) we get d=15, x=95
  Case iv:
  110 is the 2ndstandard deviation to right of mean
  x+2d=110
  solving this with eqn(1) we get d=12, x=86
  Case v:
  110 is the 3rd standard deviation to right of mean
  x+3d=110
  solving this with eqn(1) we get d=10, x=80
  Thus from the options, answers are (A)80 (C)86 (D) 95
  
  
  
  
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