Question

On the math portion of the sat, the mean score was 510 with a standard deviation of 95. on the verbal portion, the mean score was 530 with a standard deviation of 85. you now know the mean of the combined score is 1040 with a standard deviation of 127.48. given that these are normal distributions, you can do normal calculations with the combined statistics. what is the probability that a random student scored 1100 or better?

Answer 1

the probability that a random student scored 1100 or better will be found as follows:
z-score is given by:
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
thus the z-score for this situation will be:
z=(1100-1040)/127.48
z=0.4707
Thus:
P(x>1100)=1-P(z<0.4707)=1-0.6808=0.3192