Z score transformation

The annual salary of an entry-level statistics major (in thousands of dollars) is normally distributed with a mean of 75 and a standard deviation of 12. X ∼ N ( μ = 75, σ = 12 ). What is the minimum salary a statistics major should aim for in order to earn amongst the top 10%?

Correct answer:

m10 =  90.36

Step-by-step explanation:

μ=75 σ=12  X  N ( μ = 75 , σ = 12 )  p10=100%10%=110010=0.9  p(z<z10) = 1  0.1 = 0.9  z10=1.28  z10 =  σm10μ  m10=z10 σ+μ=1.28 12+75=252259=90259=90.36

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