Question

SAT scores (out of 1600) are distributed normally with a mean of 1100 and a standard deviation of 200. Suppose a school council awards a certificate of excellence to all students who score at least 1350 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 1500?

Answer 1

Answer:

0.91517

Step-by-step explanation:

Given that SAT scores (out of 1600) are distributed normally with a mean of 1100 and a standard deviation of 200. Suppose a school council awards a certificate of excellence to all students who score at least 1350 on the SAT, and suppose we pick one of the recognized students at random.

Let A - the event passing in SAT with atleast 1500

B - getting award i.e getting atleast 1350

Required probability = P(B/A)

= P(X>1500)/P(X>1350)

X is N (1100, 200)

Corresponding Z score = $\frac{x-1100}{200}$

$P(X>1500)/P(X>1350)\\= \frac{P(Z>2)}{P(Z>1.25} \\=\frac{0.89435}{0.97725} \\=0.91517$