probability SAT scores

Question

For students who graduated from high school in 2013, their SAT math scores were approximately normally distribution with a mean 0f 514 points and a standard deviation of 118 points.

 

1. if a student is randomly selected from those who graduated high school in 2013 and took the SAT, what is the probability that the student's math score was between 500 and 600 points? Write the answer as a decimal, rounded to the ten-thousandths place.
2. If a student is randomly selected from those who graduated high school in 2013 and took, the SAT,  what is the probability that the students math score was less than 400 points? Write the answer as a decimal, rounded to the ten-thousandths place.  
3. Would a SAT math score of 720 be considered unusual? please show a calculation that confirms your answer. Write the answer as a decimal, rounded to the ten-thousandths place. 

Answer 1

mean 514

sd= 118

how many between 500 to 600

z500= (500-514)/118=-0.118644

o.o47221 = under curve area, use z tables

z600= (600-514)/118=0.728813

.26694 under curve

add areas under the curve

.26694+.047221=.314161 = 31.4161% between 500 and 600

less than 400?

z400= (400-514)/118= -114/118= -0.96610169

under curve =.5-.33399= .11101= 11.101%

z720= (720-514)/118= 206/118 <2, not that unusual