Finite Math: Finding minimum score requirement

Question

A teacher says that the top 10% of the class received an A on the last test. The scores were normally distributed with mean 60 and standard deviation 12. Find the minimum score required to get an A.Fi

Answer 1

What Z score is associated with area 0.9 (90%)?

 

Calculator command invnorm(0.9) = 1.28155 gives the Z score associated with 90% of the distribution below (& 10% above).     Calculator: TI-83

 

Z = (x - μ) / σ ; putting Z = 1.28155, x = score (unknown), μ = 60, σ = 12 and solving for x, we get 75.38 or above for A.  (Better round up to 76 to be save)