Question

A teacher says that the top 9 9​% of the class received an A on the last test. The scores were normally distributed with mean 73 73 and standard deviation 14 14. Find the minimum score required to get an A.

Answer 1

z score corresponding to top 9% means the percentile score of 91% because top 9% is above bottom 91%.

so, z score for 91 percentile is 1.341 (using percentile table)

mean = 73 and standard deviation = 14

Let a be the required minimum score to get an A

using the equation

this implies

a = (1.341*14) + 73

= 18.774 + 73

= 91.774

Rounding it to 1 decimal place, we get 91.8

So, minimum score required to get an A is 91.8 (rounded to 1 decimal) or 92 (rounded to nearest decimals)