Suppose that IQ scores in one region are normally distributed with a standard deviation of . Suppose also that exactly of the individuals from this region have IQ scores of greater than (and that do not). What is the mean IQ score for this region

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answer : 101.8

Step-by-step explanation:

Given data :

Standard deviation ( б ) = 14

55% have IQ scores > 100

45% have IQ scores < 100

Determine the mean IQ score for the region

P ( X > x ) =

P ( Z ≥ ( 100 - μ ) / 14 ) = 0.55    also

P ( Z ≤ ( 100 - μ ) / 14 ) = 0.45

using standard normal calculator

100 - μ  / 14  = Z₀.₄₅ = - 0.126

resolving the relation above

100 - μ  / 14  = - 0.126

μ = 100 - 14 ( -0.126 )

   = 101.764 ≈ 101.8

a c

step-by-step explanation: