The information provided in the image states that the average composite ACT score is 20.8, with a standard deviation of 5.8. This means that most students score within 5.8 points of the average score. We can create a normal distribution curve to visualize how the scores are likely to be distributed.
Creating the Normal Distribution Curve
Label the axes: The horizontal axis should be labeled "ACT Score," and the vertical axis should be labeled "Density."
Mark the mean: The mean score, 20.8, should be marked on the horizontal axis with a line.
Mark the standard deviation: One standard deviation below the mean is 15, and one standard deviation above the mean is 26.6. These values should be marked on the horizontal axis with lines. Two standard deviations below the mean is 9.2, and two standard deviations above the mean is 32.4. These values can also be marked for additional reference.
Shade the curve: The curve should be shaded to show that the probability of getting a score within one standard deviation of the mean is highest, and the probability of getting a score further from the mean is lower.
The average ACT score is 20.8. The scores are normally distributed, with 68% of the scores falling within 1 standard deviation of the mean.
Normal distribution:
A normal distribution, also known as a Gaussian distribution, is a symmetrical probability distribution that has the shape of a bell. The average score (mean) is in the center of the bell, and the scores become progressively less likely as you move away from the mean in either direction.
The normal distribution is useful for describing a wide variety of phenomena, including ACT scores, heights of people, and errors in measurements.
The question asks you to create a normal distribution curve for the ACT scores given in the image. The mean (average) score is 20.8, and the standard deviation is 5.8. The standard deviation tells you how spread out the scores are. In a normal distribution, 68% of the scores will fall within 1 standard deviation of the mean. So, in this case, 68% of the scores will be between 15 and 26.6.