Out of the following curves, normal distribution is shown by

Question

BlackTom AI · Accepted Answer

Let’s examine each option in turn, using what the plot shows about the shapes of the curves.
Option 1: 'red curve only' — If we claim only the red curve is normal, we must justify that the red curve is the only one with the classic bell-shaped symmetry and other curves are not. However, in the figure the blue curve also displays a bell-shaped, symmetrical shape around its center, which is a hallmark of a normal distribution. Therefore, this option is unlikely because it overlooks the blue curve.
Option 2: 'red and blue curves only' — This option asserts that only red and blue are normal. While both red and blue appear to have somewhat bell-like shapes, we must consider the yellow and green curves. The yellow curve is relatively smooth and spread out, and the green curve appears skewed rather than symmetric, which would deviate from a typical normal distribution. Since one curve (green) does not resemble a normal distribution, this option is not fully accurate.
Option 3: 'red, blue and yellow curves only' — This suggests yellow is normal in addition to red and blue. If the yellow curve is noticeably flatter or exhibits any skewness or kurtosis inconsistent with a normal distribution, this would undermine the claim. Visually, yellow is broader and does not exhibit the sharp symmetry of a standard normal, which makes this option questionable.
Option 4: 'all the curves' — This option proposes that every curve shown is a normal distribution, just with different parameters. Looking at the green curve, it appears skewed or flattened in a way that deviates from the symmetric bell shape typical of a normal distribution. However, depending on the context of the data (e.g., each curve representing a normal distribution with its own mean and standard deviation), it is possible to interpret the plot as depicting several normal curves differing in center and spread. If the intent of the figure is to illustrate multiple normal distributions, then all curves can be considered normal distributions albeit with different parameters. In the context of this question, the statement that all curves are normal would be supported if the green curve is also intended to be a normal curve with its own mean and standard deviation, rather than a distinctly non-normal shape.
In summary, the question requires judging normality by symmetry and bell-shaped form. The blue and red curves clearly resemble normal distributions in shape. The yellow curve, while broad, is not clearly non-normal and could be interpreted as a normal distribution with a larger standard deviation. The green curve’s shape appears to deviate more noticeably from the classic bell form, which would typically challenge a claim of normality. Given the phrasing of the options, the statement that all curves can be interpreted as normal distributions (each with its own parameters) aligns with a common educational framing where several normal curves are overlaid to compare means and variances. Therefore, the option asserting 'all the curves' can be considered correct under that interpretation.

Out of the following curves, normal distribution is shown by单项选择题

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