At Wilson High School, SAT verbal scores have approximately a normal distribution with a mean of 500 and a standard deviation of 100.

Question

(a) What proportion of the students has SAT verbal scores that are at least 600? (b) What proportion of the students has SAT verbal scores that are at least 400? (c) Find an SAT verbal score such that only 10 percent of the students have scores above that value.

Answer 1

(a) This is 1 standard deviation above the mean so

 

P(Z>1) = 1 - Z(1) = 1 - .8413 = 0.1587 

 

(b) This is 1 standard deviation below the mean so 

 

P(Z>-1) = 1 - Z(-1) = 1 - .1587 = 0.8413 

 

(c) Find the value p in the table such that 1 - p < .1  ==>  p > .9

 

The smallest value in the table with p > .9 is Z(1.29) = 0.9015  

 

So the score need to be 1.29*100 = 129 points above the mean = 500 + 129 = 629