Question #2 SAT scores (out of 2400) are distributed normally with a mean of 150
ID: 3175478 • Letter: Q
Question
Question #2 SAT scores (out of 2400) are distributed normally with a mean of 1500 and a standard deviation of 300. Suppose a school council awards a certificate of excellence to all students who score at least 1850 on the SAT. a) Suppose one student is picked at random, what is the probability that this student will receive the school council’s certificate of excellence? b) Suppose two independent students are picked at random, what is the probability that these two students will both receive the school council’s certificate of excellence? c) Suppose two independent students are picked at random, what is the probability that these two students will both NOT receive the school council’s certificate of excellence?
Explanation / Answer
a)probability that this student will receive the school council’s certificate of excellence=P(X>1850)
=1-P(X<1850)=1-P(Z<(1850-1500)/300)=1-P(Z<1.1667)=1-0.8783=0.1217
b)probability that these two students will both receive the school council’s certificate of excellence
=(0.1217)2 =0.0148
c)probability that these two students will both NOT receive the school council’s certificate of excellence
=1-0.0148=0.9852