Answer to Question #220195 in Statistics and Probability for ihatemath

Question

The math contest called the Fermat is out of 150 points. The mean score this year is 91 points with a standard deviation of 12. Students in the top 25% receive a medal. Assuming the scores are normally distributed, what mark is required to receive a medal? *

Answer 1

$P(Z<z)=0.75.$

$z=0.67.$

$\frac{x-91}{12}=0.67.$

$x=91+0.67*12=99.$

$P(X>99)=1-P(X<99)=0.25.$