SOLUTION: Suppose ACT Mathematics scores are normally distributed with a mean of 21.5 and a standard
deviation of 5.3. A university plans to award scholarships to students whose scores are
Algebra ->
Probability-and-statistics
-> SOLUTION: Suppose ACT Mathematics scores are normally distributed with a mean of 21.5 and a standard
deviation of 5.3. A university plans to award scholarships to students whose scores are
Log On
Question 1071647: Suppose ACT Mathematics scores are normally distributed with a mean of 21.5 and a standard
deviation of 5.3. A university plans to award scholarships to students whose scores are in the top 6%.
What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if
necessary Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! We calculate the z-score for probability (X < y) = (1 - 0.06) = 0.94
:
z-score = (y - 21.5) / 5.3 = 1.56 results in P ( X < y ) = 0.94
:
1.56 * 5.3 = y - 21.5
:
y = 21.5 + 8.268 = 29.768 is approximately 29.8
:
******************************************************
The minimum score required for the scholarship is 29.8
******************************************************
:
