Normal distribution calculation:
QN: A person with IQ score greater than 145 is considered to be genius with mean 100 and SD 15. What percentage of the people should have IQ between: a) 70 and 130? , b) between 85 and 115? , c) more than 130?
Ø   
Given that,
Mean= 100
Standard deviation= 15
Since the IQ score has bell shaped curve/ normal distribution,





a.      Between 70  and 130
When X=70
The z value will be,
Z=(x- µ)/σ
  = (70-100)/15
  = -2
When X=130

The z value will be,
Z=(x- µ)/σ
  = (130-100)/15
  = 2
Area= P (-2<Z<2)
The percentage of people having IQ between 70 and 130 is 96.06%
b.      Between 85 and 115?
When X=85
The z value will be,
Z=(x- µ)/σ
  = (85-100)/15
  = -1
When X=115
The z value will be,
Z=(x- µ)/σ
  = (115-100)/15
  = 1
Area=P (-1<Z<1)
The percentage of people having IQ percent between 85 and 115 is 68.26%
c.       More than 130?
When X=130
The value of Z will be,
Z=(x- µ)/σ
  = (130-100)/15
  = 2
Area= P (Z>130)
The percentage of people having IQ more than 130 is 2.227%


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