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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 SAT critical reading data with markings on the horizontal axis for ±1 standard deviation, ±2 standard deviations, and ±3 standard deviations.

A bell curve is a symmetrical curve that's the most common representation of a normal distribution. The horizontal axis is the data's scale and the vertical axis is the frequency, proportion, or percentage of the data within each interval. The curve's highest point is its mean, and its width is influenced by the standard deviation. The data points for each standard deviation can be plotted on the horizontal axis. To plot a bell curve for the SAT critical reading data with markings on the horizontal axis for ±1 standard deviation, ±2 standard deviations, and ±3 standard deviations, the following steps can be taken:

Step 1: The mean SAT mathematics score is 516, and the standard deviation is 116. Half of the data will be above 516, and half will be below it.

Step 2: Begin by drawing a horizontal line. Mark 516 in the middle of the line.

Step 3: Draw a vertical line from the midpoint of the horizontal line, which will represent the mean.

Step 4: Marking one standard deviation from the mean on either side, calculate how much one standard deviation is from the mean by multiplying the standard deviation by 1, then subtracting and adding it to the mean (516 + 116 = 632, and 516 - 116 = 400). Mark 632 on the right and 400 on the left.

Step 5: Similarly, for two standard deviations, multiply the standard deviation by 2 and subtract and add it to the mean, then mark these values on either side of the mean. Mark 748 on the right and 284 on the left.

Step 6: For three standard deviations, multiply the standard deviation by 3 and subtract and add it to the mean, then mark these values on either side of the mean. Mark 864 on the right and 148 on the left.

Step 7: Connect the dots to create the curve, and label the horizontal axis with the markings for the standard deviations.

For such more question on frequency

https://brainly.com/question/254161

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