50 students take an iq test, which has a mean of 100 and a standard deviation of 10. What would a student need to score to be in the top 95 percentile

Question

minimum score in the top 5 percent 

maximum score and still in bottom 25 percent

Answer 1

z = (x-μ)/σ

• z = z score
• x = student's score on the IQ test
• μ = mean = 100
• σ = standard deviation = 10

 

Assuming the scores are normally distributed, find the value of the z score by looking up 0.95 on a z score table (http://www.z-table.com/).  It's about z = 1.65.

 

     z = (x-μ)/σ

     1.65 = (x-100)/10

 

Solve for x.