Astudent is deciding whether to take the sat exam a second time. he received a 540 on the verbal section on his first attempt. the mean score on the verbal section was 478 with a standard deviation of 92. it is expected that the mean of the next test will be a 485 with a standard deviation of 95. what is the minimum number of points that he would have to improve his score on his second attempt in order to better his performance on the first test

the student should get at least a score of 549 in order to improve his performance on the first test

Explanation:

For the first SAT exam , the student score was 540 that meant

Z= (X - μ )/σ = (540-478 )/ 92 = 0.674

since

P(Z≤0.674 ) = 0.7498 = 74.98%

therefore the student got a score better than the 74.98% of the other students

For the second exam, in order to have the same performance , the score should be X₂ , such that

P(Z ≤0.674 ) = 0.7498

Z=(X₂ - μ₂ )/σ₂ → X₂ = Z*σ₂+μ₂ = 0.674*95+485 = 549

X₂ = 549

thus the student should get at least a score of 549 in order to improve his performance on the first test

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