Answer:
The minimum score required for the scholarship is <u>665.09</u>.
Step-by-step explanation:
We are given that 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 6%.
<em>Let X = SAT writing scores</em>
SO, X ~ N()
The z-score probability distribution is given by ;
Z = ~ N(0,1)
where, = mean score = 489
= standard deviation = 112
Now, the minimum score required for the scholarship so that students are in the top 6% is given by ;
P(X ) = 0.06 {where is the minimum score required}
P( ) = 0.06
P(Z ) = 0.06
<em>Now, in z table we will find out that critical value of X for which the area is in top 6%, which comes out to be </em><u><em>1.57224.</em></u><em> </em>
This means;
= 489 + 176.0909 = <u>665.09</u>
Therefore, the minimum score required for the scholarship is 665.09.