Answer:
The minimum score that such a student can obtain and still qualify for admission at the college = 660.1
Step-by-step explanation:
This is a normal distribution problem, for the combined math and verbal scores for students taking a national standardized examination for college admission, the
Mean = μ = 560
Standard deviation = σ = 260
A college requires a student to be in the top 35 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?
Let the minimum score that such a student can obtain and still qualify for admission at the college be x' and its z-score be z'.
P(x > x') = P(z > z') = 35% = 0.35
P(z > z') = 1 - P(z ≤ z') = 0.35
P(z ≤ z') = 1 - 0.35 = 0.65
Using the normal distribution table,
z' = 0.385
we then convert this z-score back to a combined math and verbal scores.
The z-score for any value is the value minus the mean then divided by the standard deviation.
z' = (x' - μ)/σ
0.385 = (x' - 560)/260
x' = (0.385×260) + 560 = 660.1
Hope this Helps!!!
