SOLUTION: Suppose SAT Writing scores are normally distributed with a mean of 489 and a standard deviation of 112. A university plans to award scholarships to students whose scores are in th

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose SAT Writing scores are normally distributed with a mean of 489 and a standard deviation of 112. A university plans to award scholarships to students whose scores are in th      Log On


   

Question 1168534: Suppose SAT Writing scores are normally distributed with a mean of 489 and a standard deviation of 112. A university plans to award scholarships to students whose scores are in the top 4%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.

Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Let's solve this problem step-by-step.
**1. Understand the Problem**
* SAT Writing scores are normally distributed.
* Mean (μ) = 489
* Standard deviation (σ) = 112
* We need to find the score that corresponds to the top 4%.
**2. Find the Z-score**
* We need to find the z-score that corresponds to the top 4% of the distribution.
* The top 4% means that 96% of the scores are below this point.
* We need to find the z-score corresponding to a cumulative probability of 0.96.
* Using a z-table or calculator, we find that the z-score corresponding to 0.96 is approximately 1.75.
**3. Convert the Z-score to a Raw Score**
* We use the formula: X = μ + zσ
* X = 489 + 1.75 * 112
* X = 489 + 196
* X = 685
**4. Round to the Nearest Whole Number**
* The minimum score required for the scholarship is 685.
**Therefore, the minimum score required for the scholarship is 685.**