Suppose ACT Reading scores are normally distributed with a mean of 21.221.2 and a standard deviation of 6.26.2. 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 tenth, if necessary.

The minimum score required for the scholarship is 30.95.

Step-by-step explanation:

We are given that ACT Reading scores are normally distributed with a mean of 21.2 and a standard deviation of 6.2.

A university plans to award scholarships to students whose scores are in the top 6%.

Let X = ACT Reading scores

SO, X ~ N()

The z-score probability distribution is given by ;

                  Z = ~ N(0,1)

where, = mean score = 21.2

            = standard deviation = 6.2

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 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;        

                              = 21.2 + 9.7478 = 30.95

Therefore, the minimum score required for the scholarship is 30.95.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

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