Question

A new exam was written to be used as an entrance exam. You took the exam and your score report said that you got a score of 633 points out of 800 possible and that the mean and standard deviation for all test takers is μ = 400 and σ = 100 and the distribution is normal. What percentage of students taking the test scored higher than you did?

The department decides to accept all the students who score in the top 10% of the new exam. What is the test score for their cutoff point?

Answer 1

Given that,

mean = = 400

standard deviation = =100

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10

= P(Z < z ) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.28) = 0.90

z = 1.28 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.28 *100+400

x= 528

cut off=528