Draw two normal curves that have the same mean but different s...

Question

Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences.

Accepted Answer

Hello, everyone. Let's take a look at this question together. Two normal curves are drawn on the same graph. Both have a mean of 100, but curve X as a standard deviation of 8, and curve Y as a standard deviation of 20. Which of the following statements is true? Is it answer choice A, Curve X is wider and shorter than curve Y? Answer choice B, curve Y is narrower and taller than curve X. Answer choice C. Both curves are centered at 100, but curve X is taller and narrower than curve Y, or answer choice D, curve Y is centered to the left of curve X. So in order to solve this question, we have to Recall how a standard deviation value affects a normal curve to determine which of the following statements about curve X and curve Y is true. And looking at the information provided in the question, we know that we have a mean of 100, so both curves are centered at the same point. Which is 100 on the X axis, and looking at the standard deviation of both curves, we know that curve X has a standard deviation equal to 8, and curve Y has a standard deviation equal to 20. Well, based on curve X having a standard deviation of 8, We know that this results in less variability or curve X, which makes the curve narrower and taller, whereas curve Y, which has a standard deviation equal to 20, experiences more variability which results in a wider and shorter curve. And we know that the height and the width of a normal distribution curve are determined by the standard deviation, where A smaller standard deviation tells us that the data is concentrated closer to the mean, resulting in a taller and narrower curve, whereas the larger standard deviation tells us that the data is more spread out, which results in that shorter and wider curve. Therefore, based on this information, we know that while both curves are centered at the mean of 100, Curve X is taller and narrower than curve Y due to the smaller standard deviation, which tells us that the data is concentrated closer to the mean, leading to that taller and narrower curve. And looking at our answer choices, we can identify that answer choice C is the correct answer, as It contains a true statement about curve X and curve Y, where both curves are centered at 100, but curve X is taller and narrower than curve Y. So answer choice C is the only true statement, so it is the only correct answer choice. I hope you found this video to be helpful. Thank you and goodbye.

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