Question

Questions 6-10 A recent version of the mathematics section on the SAT test was reported by the College Board to have a distribution of X N: (518,115); that is, normally distributed with a mean of 518 and a standard deviation of 115. That year, about 1.7 million (1,700,000) high school students took the SAT.

6. What is the probability that a randomly selected student from that year had a SAT math score below 440?

7. An honors program for engineering at a certain college requires at least a 720 SAT math score to be considered for admission. How many students that year met this requirement?

8. Another program only admits students with SAT math scores in the top 20%. What is the cutoff score (the lowest SAT math score) they will take for this program?

9. What SAT math score is at the 90th percentile?

10. What percent of students from that year had SAT math scores between 600 and 700?

Answer 1

Q 6)

Q 7)

The number of students that year met this requirement are = 1700000*0.0392 =66640

Q8) For top 20% the critical value of Z is 0.841

Therefore the cutoff is

Q 9) For 90th percentile the value of Z is 1.282

The SAT math score at 90th percentile is

Q 10)

Answer: 18.18% of students from that year had SAT math scores between 600 and 700