Answer :
The minimum gre score is 588.6
Define Standard normal variable
The formula z = (x-mean) / standard deviation can be used to transform any point (x) from a normal distribution to the standard normal distribution (z).The value of z for each given x value indicates how far away from the mean for all x values x is.
Given,
normally distributed with a mean μ = 459
standard deviation σ = 120
University plans to offer tutoring jobs to students whose scores are in the top = 14% or 0.14
Standard normal variable is given by,
Z = (x - μ) / σ
P(X ≥ x₁) = 0.14
⇒P( [ (x - μ)/ σ ] ≥ [ (x₁ - μ)/ σ ] ) = 0.14
⇒P( z ≥ [ (x₁ - 459)/ 120 ] ) = 0.14
⇒P( z ≥ z₁ ) = 0.14
⇒P(0 < z < z₁ ) = 0.5 - 0.14 = 0.36
From standard normal tables
z₁ = 1.08
Where, z₁ = (x₁ - 459)/ 120
1.08 = (x₁ - 459)/ 120
After solving , we get
x₁ = 588.6
Therefore, the minimum gre score is 588.6 or 589
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