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?

Question

Yair Young

Mathematics

7 September, 02:36

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?

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Madisyn Hester · 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