Question

3.16 SAT scores: SAT scores (out of 2400 ) are distributed normally with a mean of 1480 and a standard deviation of 295. Suppose a school council awards a certificate of excellence to all students who score at least 1900 on the SAT, and suppose we pick one of the recognized students at random. What is the probability this student's score will be at least 2100? (The material covered in Section 2.2 would be useful for this question.) (Keep 1 decimal place.)

Answer 1

The probability that a student's SAT score will be at least 2100 is approximately 0.0174.

Step-by-step explanation:

To find the probability that a student's SAT score is at least 2100, we need to standardize the score using the z-score formula and then find the corresponding area under the standard normal curve. First, we calculate the z-score: z = (2100 - 1480) / 295 = 2.1017. Using a standard normal distribution table or a calculator, we find that the area to the left of z = 2.1017 is approximately 0.9826. Since the probability that the student's score is at least 2100 is equal to 1 minus the probability to the left of 2100, we subtract 0.9826 from 1: 1 - 0.9826 ≈ 0.0174.