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Many students take standardized tests for college applications. They are called standardized tests because they are scored so the population of student scores for any one particular test follows a normal distribution. The most common test are the SAT and the ACT.

Suppose the mean and standard deviation for the ACT composite score, the SAT critical reading score, and the SAT mathematics score for the year 2017 are as follows:

For the ACT, the mean composite score was 21.0 with a standard deviation of 5.2.

For the SAT critical reading score, the mean was 501 with a standard deviation of 112.

For the SAT mathematics score, the mean was 516 with a standard deviation of 116.

Sketch a bell curve for the ACT composite data with markings on the horizontal axis for ±1 standard deviation, ±2 standard deviations, and ±3 standard deviations.

A bell curve graph for the ACT composite data with markings on the horizontal axis for ±1 standard deviation, ±2 standard deviations, and ±3 standard deviations is shown below:

Image result for bell curve for ACT composite dataIn this bell curve graph, the horizontal axis represents the ACT composite scores. The peak of the curve, at x = 21, represents the mean ACT composite score of 21.0. The vertical axis represents the frequency of students who achieved each score, with the highest point of the curve representing the most frequent score of 21.0.

The standard deviation of 5.2 is used to draw the lines representing ±1, ±2, and ±3 standard deviations from the mean. These lines are plotted at distances of 5.2, 10.4, and 15.6 units, respectively, from the mean on either side of the graph.

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