To enroll in intermediate algebra, a student at the College of San Mateo (CSM) must score at least 21 points (out of 50) on a placement test. Using four semesters of data, the CSM Mathematics Department computed the percentages of students who succeeded in intermediate algebra (grade of A, B, or C) for various groups of scores on the placement test (see Table 26).

Let p be the percentage of intermediate algebra students succeeding in the course who scored x points on the placement test.
a. Construct a scatterplot.
b. Find an equation of a linear model.
c. Students who score below 21 points (out of 50) on the placement test cannot enroll in intermediate algebra. Use the model to predict how high the cutoff score would have to be to ensure that all students succeed in the course. Do you have much faith in your prediction? Explain.
d. Use the model to predict for which scores no students would succeed in the course. Do you have much faith in your prediction? Explain.
e. If, in one semester, 145 students scored in the 16€“20-point range on the placement test, predict how many of these students would have succeeded in the course if they had been allowed to enroll in it. Assuming your prediction is accurate, would you advise CSM to lower the placement score cutoff to 16? Explain.

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Table 26 Percentages of Intermediate Algebra Students Who Succeeded Score Used to Represent Score GroupIntermediate Algebra Percentage Who Succeeded in Placement Score Group 21-25 26-30 31-35 36-40 41-45 46-50 23 28 34 47 38 43 48 71 84