the math sat scores for women are normally distributed with a mean of 496 and a standard deviation of 108.

Question

 if a woman who takes the math portion of the sat is randomly selected what is the probability that her score is above 500

Answer 1

we know that:

mu = 496

sd = 108

 

x= 500

 

then:

 

P (x>500) = 1 - P( x<=500) = 1 - P( Z <= (500 - mu)/sd) = 1 - P (Z<= (500-496)/108) 

P(x> 500) = 1 - P (Z<= 0.03) = 1 - 0.48 = 0.52

 

we get the value of P(Z<=0.03) either from Standard Gaussian Distribution table, or from calculator, or computer software,

 

There is 52% chance that she get 500 or more on the test.