Question

SAT scores (out of 1600) are distributed normally with a mean of 1100 and a standard deviation of 210. Suppose a school council awards a certificate of excellence to all students who

score at least 1370 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 1535?

Answer 1

See below

Explanation:

1370 is 270 points ABOVE the mean

this is 270 /210 = z-score = +1.286

use z-score table to find this corresponds to ~.900

1535 is z-score : 2.071 corresponding to ~ .981

.981-.900 = .081 = 8.1%