90 95 99 rule and percents

Question

Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with µ=111 and σ=21 .

Enter the score which marks the lowest 25 percent of the distribution. 

Enter the score which marks the highest 5 percent of the distribution. 

Answer 1

Lowest 25%

Find z score for P=.2500 from the Z table

The result is -0.674

X = Z* Std Dev + Mean

X= (-.674)*21 +111 = -14.2 + 111 = 96.8

Lowest 25% marked by a score of 96.8

Highest 5%

Find z score for P=.9500 from the Z table

The result is 1.645

X = Z* Std Dev + Mean

X= (1.645)*21 +111 = 34.5 + 111 = 145.5

Highest 5% marked by a score of 145.5