MathCastle
Statistics & DataChallengeThe Normal Distribution

The Normal Distribution · Challenge problem

Exam scores are normal. The top 10%10\% earn an A, which requires at least 8888 points, and the bottom 10%10\% fail, which means scoring below 5656. Using Φ(1.28)=0.90\Phi(1.28) = 0.90 and Φ(0.64)=0.7389\Phi(0.64) = 0.7389, what fraction of students score between 6464 and 8080? Give four decimal places.