2. Knowing the results of the 2018 SAT math exam with a mean of 531 and standard deviation of 114, answer the following questions: (10 points) a. What percentage of test takers scored lower than 400 on the math SAT?
Your calculation:

b. What percentage scored between 600 and 700 points?
Your calculation:

c. Your score is 725. What is your percentile rank?

(a) 12.5%

(b) 20%

(c) 96th

Step-by-step explanation:

Let X denote the results of the 2018 SAT math exam.

It is provided that the mean of exam was, μ = 531 and standard deviation of σ  114.

Assume that X follows a normal distribution.

(a)

Compute the probability of test takers who scored lower than 400 on the math SAT as follows:

Thus, the percentage of test takers who scored lower than 400 on the math SAT is 12.5%.

(b)

Compute the probability of test takers who scored between 600 and 700 points as follows:

Thus, the percentage of test takers who scored between 600 and 700 points is 20%.

(c)

Compute the value of P (Z < 725) as follows:

Thus, a student who scores 725 has a 96th percentile rank.