Question

Assume math scores on the SAT are normally distributed with a mean of 500 and a standard deviation of 100. 

a. What is the probability that one randomly selected individual taking the sat will have a Math score of more than 530? 

b. What is the probability that one randomly selected individual taking the SAT will have a Math score between 450 and 600?

c. Find the 60th percentile of these scores.

Answer 1

For given information math scors on the SAT are normally distributed with a mean = 500 stabdard devuatuion=100

a) To find the probability that SAT will have math score of more than 530, the mathematical form is bellow.

  =

to find the z score the formula is   ,   

z=0.3

z follows normal with mean=0 and standard deviaton =1

1- P(z<= 0.3)= 0.382

The probabilty that SAT will have math score of more than 530 is 0.382

b) to find probability of  the SAT will have math score between 450 and 600. The mathematical form is bellow

=  

= 0.84134 - 0.3085=0.5328

The probability of  the SAT will have math score between 450 and 600 is 0.5328

c) To find the 60th percentile of these scores. that is which data value that have 60% data are bellow.

It is probabilty is 0.60 it is that means   P(z<= (x-500)/100) = 0.60

and z value is 0.25 with corresponding probability is 0.60.

x= 0.25*100+500 = 525

The 60th percentile of the scores is 525.

Answer 2

What is the probability of having an SAT score of 91 or less?