Suppose SAT Writing scores are normally distributed with a mean of 489489 and a standard deviation of 112112. A university plans to award scholarships to students whose scores are in the top 6%6%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.

The minimum score required for the scholarship is 665.09.

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%.

Let X = SAT writing scores

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

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 1.57224.

This means;        

                              = 489 + 176.0909 = 665.09

Therefore, the minimum score required for the scholarship is 665.09.

the expression (1.26)2t reveals the approximate rate of increases in the number of plants semiannually.

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step-by-step explanation: