Question

People with​ z-scores of 2.25 or above on a certain aptitude test are sometimes classified as geniuses. if aptitude test scores have a mean of 100 and a standard deviation of 12 ​points, what is the minimum aptitude test score needed to be considered a​ genius

Answer 1

Let the minimum score be x
z-score is given by:
z=(x-μ)/σ
where:
mean,μ=100
standard deviation, σ=12
z=2.25
thus
2.25=(x-100)/12
solving for x we get:
27=x-100
x=100+27
x=127
Thus the minimum test score is 127 points